A109570 E.g.f.: x/(1-sinh(x)).

0, 1, 2, 6, 28, 160, 1086, 8624, 78296, 799488, 9070810, 113208832, 1541351604, 22734473216, 361121134934, 6145880954880, 111569141960752, 2151953994809344, 43948641637067058, 947412315736506368

Offset

0,3

Comments

"Bernoulli numbers" for x/(1-sinh(x)).

Links

Table of n, a(n) for n=0..19.

Formula

E.g.f. x/(1-sinh(x)).

From Sergei N. Gladkovskii, May 30 2012: (Start)

Let E(x)=x/(1-sinh(x)) be the e.g.f., then

E(x)=- 1 + 1/(1-x)+ x^4/((1-x)*((1-x)*G(0) - x^2)) ; G(k)= (2*k+2)*(2*k+3)+x^2-(2*k+2)*(2*k+3)*x^2/G(k+1); (continued fraction, Euler's kind, 1-step).

E(x)= -1 + 1/(1-x)+ x^4/((1-x)*((1-x)*G(0) - x^2)) ; G(k)= 8*k+6+x^2/(1 + (2*k+2)*(2*k+3)/G(k+1)); (continued fraction, Euler's 2nd kind, 2-step).

E(x)= x/(1 - x*G(0)); G(k)= 1 + x^2/(2*(2*k+1)*(4*k+3) + 2*x^2*(2*k+1)*(4*k+3)/(-x^2 - 4*(k+1)*(4*k+5)/G(k+1))); (continued fraction).

(End)

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

Maple

G:=x/(1-sinh(x)): Gser:=series(G, x=0, 25): 0, seq(n!*coeff(Gser, x^n), n=1..22);

Mathematica

g[x_] = x/(-1 + Sinh[x]) h[x_, n_] = Dt[g[x], {x, n}] a[x_] = Table[ -h[x, n], {n, 0, 50}]; b = a[0]
With[{nn=20}, CoefficientList[Series[x/(1-Sinh[x]), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Jul 02 2017 *)

Crossrefs

Sequence in context: A201950 A358265 A356633 * A262002 A245633 A345367

Adjacent sequences: A109567 A109568 A109569 * A109571 A109572 A109573

Keyword

nonn

Author

Roger L. Bagula, Jun 27 2005

Status

approved