A203709 E.g.f.: 2*Product_{n>=1} ((exp(x^n) + 1)/2).

2, 1, 3, 10, 55, 311, 2446, 19447, 196337, 2014777, 24828706, 311108051, 4507990477, 66719239237, 1112079627842, 18945126606421, 356368711926481, 6867187345103057, 143985206958508162, 3092256807348721807, 71426909592196938101, 1691486262041519369581

Offset: 0

Author

Paul D. Hanna, Jan 04 2012

Keywords

• nonn

Examples

			E.g.f.: A(x) = 2 + x + 3*x^2/2! + 10*x^3/3! + 55*x^4/4! + 311*x^5/5! +...
where
A(x) = 2*(exp(x)+1)/2 * (exp(x^2)+1)/2 * (exp(x^3)+1)/2 * (exp(x^4)+1)/2 *...
The log of the e.g.f. begins:
log(A(x)/2) = (x/2)/(1-x^2) + 5*(x/2)^2/2! + 238*(x/2)^4/4! + 28816*(x/2)^6/6! + 6397168*(x/2)^8/8! + 2322439936*(x/2)^10/10! +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..440

Crossrefs

Cf. A203716, A270665.

Programs

Mathematica

nmax = 25; Range[0, nmax]! * CoefficientList[Series[2*Product[1/(1 - Tanh[x^k/2]), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 21 2016 *)

PARI

{a(n)=n!*polcoeff(2*prod(k=1,n,(exp(x^k+x*O(x^n))+1)/2),n)}