A198513 E.g.f.: Sum_{n>=0} sinh(n*x)^n/n!.

1, 1, 4, 28, 320, 5556, 129600, 3756936, 132872192, 5679982288, 286769980416, 16732506817280, 1115928688967680, 84383735744758464, 7163164003950936064, 676619301019539271040, 70674282825174467215360, 8117559039240651749888256

Offset: 0

Author

Paul D. Hanna, Oct 26 2011

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 4*x^2/2! + 28*x^3/3! + 320*x^4/4! + 5556*x^5/5! +...
where
A(x) = 1 + sinh(x) + sinh(2*x)^2/2! + sinh(3*x)^3/3! + sinh(4*x)^4/4! +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..260

Crossrefs

Cf. A108459.

Programs

PARI

{a(n)=local(A=sum(m=0,n,sinh(m*x+x*O(x^n))^m/m!));n!*polcoeff(A,n)}

Formula

E.g.f.: Sum_{n>=0} exp(-n^2*x) * (exp(2*n*x) - 1)^n / (2^n*n!).