A107404 Expanison of e.g.f. 1/(1 - sinh(x))^2.

1, 2, 6, 26, 144, 962, 7536, 67706, 685824, 7730882, 95970816, 1300815386, 19113775104, 302616787202, 5135568746496, 92996021795066, 1789758460329984, 36479831022049922, 785020114093080576, 17785273588395966746, 423150055005134782464, 10548427254444904799042

Offset

0,2

Links

Table of n, a(n) for n=0..21.

Formula

a(n) = D^n(1/(1-x)^2) evaluated at x = 0, where D is the operator sqrt(1+x^2)*d/dx. Cf. A006154. - Peter Bala, Dec 06 2011

a(n) ~ n!*n/(2*(log(1+sqrt(2)))^(n+2)). - Vaclav Kotesovec, Jun 27 2013

a(n) = Sum_{k=0..n} (k+1)! * A136630(n,k). - Seiichi Manyama, Feb 17 2025

Maple

E(x):=1/(1-sinh(x))^2: f[0]:=E(x): for n from 1 to 30 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..30);

Mathematica

CoefficientList[Series[1/(1-Sinh[x])^2, {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 27 2013 *)

Prog

(PARI) a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (k+1)!*a136630(n, k)); \\ Seiichi Manyama, Feb 17 2025

Crossrefs

Cf. A000557. A006154, A136630.

Sequence in context: A177381 A289312 A127116 * A120574 A333044 A178324

Adjacent sequences: A107401 A107402 A107403 * A107405 A107406 A107407

Keyword

nonn,changed

Author

Miklos Kristof, Jun 09 2005

Status

approved