A134200 E.g.f. satisfies: A(x) = x*(exp(sinh(A(x)))).

0, 1, 2, 9, 68, 725, 9942, 166453, 3290632, 75017097, 1937420010, 55906879809, 1782695466444, 62247810769053, 2362246665531326, 96806321000599725, 4260677055123222544, 200440759819510706321, 10037364633737549049042, 533071599267242747118585

Offset: 0

Author

Alois P. Heinz, Aug 27 2008

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..300

Programs

Maple

A:= proc(n) option remember; if n=0 then 0 else convert (series (x* (exp (sinh(A(n-1)))), x=0, n+1), polynom) fi end: a:= n-> coeff (A(n), x, n)*n!: seq (a(n), n=0..30);

Mathematica

CoefficientList[InverseSeries[Series[x/E^Sinh[x],{x,0,20}],x],x] * Range[0,20]! (* Vaclav Kotesovec, Jul 16 2014 *)

Maxima

a(n):=if n<2 then n else sum(((sum((-1)^i*(k-2*i)^(n-1) *binomial(k,i), i,0,k))*n^k)/(2^k*k!),k,1,n-1); /* Vladimir Kruchinin, May 10 2011 */

Formula

a(n) = sum(k=1..n-1, ((sum(i=0..k, (-1)^i*(k-2*i)^(n-1)* C(k,i))) *n^k)/(2^k*k!)), a(0)=0, a(1)=1. - Vladimir Kruchinin, May 10 2011

a(n) ~ n^(n-1) / (exp(n) * r^n * sqrt(1/s^2+sinh(s))), where r = 0.3296546568511367672... and s = 0.7650099545507321226... are roots of the system of equations exp(sinh(s))*r = s, s*cosh(s) = 1. - Vaclav Kotesovec, Jul 16 2014