The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A198631

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A198631

Numerators of the rational sequence with e.g.f. 1/(1+exp(-x)).
(history; published version)

#84 by Peter Luschny at Fri Feb 23 01:46:44 EST 2024

STATUS

proposed

approved

#83 by Werner Schulte at Fri Feb 16 15:54:48 EST 2024

STATUS

editing

proposed

Discussion

Sat Feb 17

17:08

Peter Luschny: I don't understand this linguistically: "r(n) =  ... where r(n) = ..."?

Sun Feb 18

04:01

Werner Schulte: The author, Wolfdieter Lang, used "r(n)", see FORMULA and EXAMPLE. So I did. It's the same rational sequence, i.e., r(n) <> a(n).

#82 by Werner Schulte at Fri Feb 16 15:54:13 EST 2024

FORMULA

Conjecture: r(n) = Sum_{k=0..n} A001147(k) * A039755(n, k) * (-1)^k / (k+1) where r(n) = a(n) / A006519(n+1) = (n!) * ([x^n] (2 / (1 + exp(-x)))), for n >= 0. - Werner Schulte, Feb 16 2024

STATUS

approved

editing

#81 by Peter Luschny at Tue Jul 21 11:48:00 EDT 2020

STATUS

proposed

approved

#80 by Michel Marcus at Tue Jul 21 10:41:54 EDT 2020

STATUS

editing

proposed

#79 by Michel Marcus at Tue Jul 21 10:41:44 EDT 2020

FORMULA

a(n) = -2*Zetazeta(-n)*A335956(n+1). - Peter Luschny, Jul 21 2020

STATUS

proposed

editing

#78 by Peter Luschny at Tue Jul 21 08:06:12 EDT 2020

STATUS

editing

proposed

#77 by Peter Luschny at Tue Jul 21 08:06:00 EDT 2020

FORMULA

a(n) = -2*Zeta(-n)*A335956(n+1). - Peter Luschny, Jul 21 2020

STATUS

proposed

editing

#76 by Peter Luschny at Tue Jul 21 08:00:40 EDT 2020

STATUS

editing

proposed

#75 by Peter Luschny at Tue Jul 21 08:00:37 EDT 2020

FORMULA

a(n) = -Zeta(-n)*A335956(n+1). _- _Peter Luschny_, Jul 21 2020

STATUS

proposed

editing