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%I #15 Mar 21 2016 07:57:36
%S 2,1,3,10,55,311,2446,19447,196337,2014777,24828706,311108051,
%T 4507990477,66719239237,1112079627842,18945126606421,356368711926481,
%U 6867187345103057,143985206958508162,3092256807348721807,71426909592196938101,1691486262041519369581
%N E.g.f.: 2*Product_{n>=1} ((exp(x^n) + 1)/2).
%H Vaclav Kotesovec, <a href="/A203709/b203709.txt">Table of n, a(n) for n = 0..440</a>
%e E.g.f.: A(x) = 2 + x + 3*x^2/2! + 10*x^3/3! + 55*x^4/4! + 311*x^5/5! +...
%e where
%e A(x) = 2*(exp(x)+1)/2 * (exp(x^2)+1)/2 * (exp(x^3)+1)/2 * (exp(x^4)+1)/2 *...
%e The log of the e.g.f. begins:
%e 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! +...
%t 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 *)
%o (PARI) {a(n)=n!*polcoeff(2*prod(k=1,n,(exp(x^k+x*O(x^n))+1)/2),n)}
%Y Cf. A203716, A270665.
%K nonn
%O 0,1
%A _Paul D. Hanna_, Jan 04 2012
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