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%I #11 Nov 02 2014 05:58:23
%S 1,1,6,88,2280,92416,5393376,428428288,44450655360,5836916064256,
%T 946245183223296,185613384522661888,43330332249288714240,
%U 11871318610487327850496,3772031142226151742038016,1375871976238663365598117888
%N E.g.f.: Sum_{n>=0} Product_{k=1..n} tanh((2*k-1)*x).
%H Vaclav Kotesovec, <a href="/A218260/b218260.txt">Table of n, a(n) for n = 0..150</a>
%F E.g.f.: Sum_{n>=0} Product_{k=1..n} (1 - exp(-2*(2*k-1)*x)) / (1 + exp(-2*(2*k-1)*x)).
%F a(n) ~ 2^(4*n+7/2) * n^(2*n+1) / (exp(2*n) * Pi^(2*n+1)). - _Vaclav Kotesovec_, Nov 02 2014
%e E.g.f.: A(x) = 1 + x + 6*x^2/2! + 88*x^3/3! + 2280*x^4/4! + 92416*x^5/5! +...
%e where
%e 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) +...
%o (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)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A002105, A221080.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Oct 24 2012
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