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%I #5 Oct 30 2014 17:14:52
%S 1,-154,22885622,-67465813019194,1437168237462688869782,
%T -134874257420380161852790174234,
%U 41492847795963159872255018412799196342,-34364863511758593932657779153553482763524487674,66563566600887661498498837311669792149014849464660729302
%N E.g.f.: Sum_{n>=0} exp(n^2*(n+1)/2*x) / (1 + exp(n^2*x))^(n+1) = Sum_{n>=0} a(n) * x^(2*n) / (2*n)!.
%C Compare to an e.g.f. of A248656: Sum_{n>=0} exp(n*(n+1)/2*x)/(1 + exp(n*x))^(n+1).
%e E.g.f.: A(x) = 1 - 154*x^2/2! + 22885622*x^4/4! - 67465813019194*x^6/6! +-...
%e where
%e A(x) = 1/2 + exp(x)/(1+exp(x))^2 + exp(6*x)/(1+exp(4*x))^3 + exp(18*x)/(1+exp(9*x))^4 + exp(40*x)/(1+exp(16*x))^5 + exp(75*x)/(1+exp(25*x))^6 +...
%o (PARI) \p200 \\ set precision
%o {A=Vec(serlaplace(sum(n=0,800,1.*exp(n^2*(n+1)/2*x +O(x^31))/(1 + exp(n^2*x +O(x^31)))^(n+1)) ))}
%o for(n=1,#A\2,print1(round(A[2*n-1]),", "))
%Y Cf. A248656.
%K sign
%O 0,2
%A _Paul D. Hanna_, Oct 26 2014
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