Revision History for A091345
(Underlined text is an addition;
strikethrough text is a deletion.)
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#6 by Vaclav Kotesovec at Tue May 07 04:01:20 EDT 2019
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#5 by Vaclav Kotesovec at Tue May 07 04:00:54 EDT 2019
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#4 by Vaclav Kotesovec at Tue May 07 03:57:25 EDT 2019
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#3 by Vaclav Kotesovec at Tue May 07 03:56:52 EDT 2019
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| MATHEMATICA
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nmax = 20; CoefficientList[Series[(E^x-1)^2 / (2-E^x)^4, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, May 07 2019 *)
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| STATUS
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approved
editing
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#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006
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| FORMULA
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a(n)=Sum(C(n,, k)Sum(i!i Stirling2(k,, i), i=1,..,, .., k)Sum(i!i Stirling2(n-k,, i), i=1,..,, .., n-k), k=0,..,, .., n)
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| MATHEMATICA
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Table[ Sum[Binomial[n, , k]Sum[i!i StirlingS2[k, , i], {i, , 1, , k}]Sum[i!i StirlingS2[n - k, i], {i, 1, n - k}], {k, 0, n}], {n, 0, 20}]
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| KEYWORD
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easy,nonn,new
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#1 by N. J. A. Sloane at Thu Feb 19 03:00:00 EST 2004
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| NAME
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Exponential convolution of A069321(n) with itself, where we set A069321(0)=0.
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| DATA
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0, 0, 2, 30, 398, 5430, 79022, 1238790, 20944478, 381167670, 7443745742, 155454939750, 3459933837758, 81801569650710, 2048133412585262, 54153668865539910, 1508122968767710238, 44130728380569410550
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| OFFSET
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0,3
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| FORMULA
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a(n)=Sum(C(n,k)Sum(i!i Stirling2(k,i), i=1,..,k)Sum(i!i Stirling2(n-k,i), i=1,..,n-k), k=0,..,n)
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| MATHEMATICA
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Table[ Sum[Binomial[n, k]Sum[i!i StirlingS2[k, i], {i, 1, k}]Sum[i!i StirlingS2[n - k, i], {i, 1, n - k}], {k, 0, n}], {n, 0, 20}]
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| KEYWORD
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easy,nonn
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| AUTHOR
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Mario Catalani (mario.catalani(AT)unito.it), Jan 01 2004
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| STATUS
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approved
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