A248656 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)!.

1, -4, 1172, -2394604, 17925470132, -356711164156204, 15557257046545589492, -1306859934761006954164204, 192757826813283097789632563252, -46564510721452609888686654192978604, 17449940281041871638688960825766828695412, -9712709908164237387647891995373875626734039404

Offset: 0

Author

Paul D. Hanna, Oct 26 2014

Keywords

• sign

Comments

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

Examples

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

Crossrefs

Cf. A122399, A248657.

Programs

PARI

\p100 \\ set precision
{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)) ))}
for(n=1,#A\2,print1(round(A[2*n-1]),", "))