A248656 - OEIS

%I #9 Oct 30 2014 17:14:33

%S 1,-4,1172,-2394604,17925470132,-356711164156204,15557257046545589492,

%T -1306859934761006954164204,192757826813283097789632563252,

%U -46564510721452609888686654192978604,17449940281041871638688960825766828695412,-9712709908164237387647891995373875626734039404

%N E.g.f.: Sum_{n>=0} exp(n*(n+1)/2*x) / (1 + exp(n*x))^(n+1)  =  Sum_{n>=0} a(n) * x^(2*n) / (2*n)!.

%C Compare to an e.g.f. of A122399: Sum_{n>=0} exp(n^2*x)/(1 + exp(n*x))^(n+1).

%e E.g.f.: A(x) = 1 - 4*x^2/2! + 1172*x^4/4! - 2394604*x^6/6! + 17925470132*x^8/8! -+...

%e where

%e A(x) = 1/2 + exp(x)/(1+exp(x))^2 + exp(3*x)/(1+exp(2*x))^3 + exp(6*x)/(1+exp(3*x))^4 + exp(10*x)/(1+exp(4*x))^5 + exp(15*x)/(1+exp(5*x))^6 + exp(21*x)/(1+exp(6*x))^7 +...

%o (PARI) \p100 \\ set precision

%o {A=Vec(serlaplace(sum(n=0,800,1.*exp((n^2+n)/2*x +O(x^31))/(1 + exp(n*x +O(x^31)))^(n+1)) ))}

%o for(n=1,#A\2,print1(round(A[2*n-1]),", "))

%Y Cf. A122399, A248657.

%K sign

%O 0,2

%A _Paul D. Hanna_, Oct 26 2014