A218260 E.g.f.: Sum_{n>=0} Product_{k=1..n} tanh((2*k-1)*x).

1, 1, 6, 88, 2280, 92416, 5393376, 428428288, 44450655360, 5836916064256, 946245183223296, 185613384522661888, 43330332249288714240, 11871318610487327850496, 3772031142226151742038016, 1375871976238663365598117888

Offset: 0

Author

Paul D. Hanna, Oct 24 2012

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 6*x^2/2! + 88*x^3/3! + 2280*x^4/4! + 92416*x^5/5! +...
where
A(x) = 1 + tanh(x) + tanh(x)*tanh(3*x) + tanh(x)*tanh(3*x)*tanh(5*x) + tanh(x)*tanh(3*x)*tanh(5*x)*tanh(7*x) +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..150

Crossrefs

Cf. A002105, A221080.

Programs

PARI

{a(n)=local(X=x+x*O(x^n),Egf);Egf=sum(m=0,n,prod(k=1,m,tanh((2*k-1)*X)));n!*polcoeff(Egf,n)}
for(n=0,30,print1(a(n),", "))

Formula

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

a(n) ~ 2^(4*n+7/2) * n^(2*n+1) / (exp(2*n) * Pi^(2*n+1)). - Vaclav Kotesovec, Nov 02 2014