OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..427
FORMULA
a(n) = Sum_{k=1..n} Sum_{i=0..k} (-1)^i*(k-2*i)^n*binomial(k,i), n>0, a(0)=1.
a(n) ~ n! /(sqrt(5)*(log(2+sqrt(5))/2)^(n+1)). - Vaclav Kotesovec, Jun 26 2013
a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} 4^k * binomial(n,2*k+1) * a(n-2*k-1). - Seiichi Manyama, Jun 30 2022
MATHEMATICA
CoefficientList[Series[1/(1-Sinh[x]*Cosh[x]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)
PROG
(Maxima) a(n):=sum(sum((-1)^i*(k-2*i)^n*binomial(k, i), i, 0, k), k, 1, n);
(PARI) my(x='x+O('x^30)); Vec(serlaplace(1/(1 - sinh(x)*cosh(x)))) \\ Michel Marcus, Jun 30 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, May 29 2011
STATUS
approved