A135747 E.g.f.: A(x) = Sum_{n>=0} exp( (n^2-1)*x ) * x^n/n!.

1, 0, 2, 9, 88, 985, 14976, 278929, 6208000, 163268865, 4979147680, 173500986241, 6838921208736, 302161792811905, 14840867887070512, 804732692174218305, 47888731015720316416, 3110871265807567331329, 219546952410733092279360

Offset: 0

Author

Paul D. Hanna, Nov 27 2007

Keywords

• nonn

Comments

n divides a(n) for n>=1.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Crossrefs

Cf. variants: A135742, A135743, A135744, A135745, A135746.

Programs

Mathematica

Flatten[{1, Table[Sum[Binomial[n, k]*(k^2 - 1)^(n - k), {k, 0, n}], {n,1,25}]}] (* G. C. Greubel, Nov 05 2016 *)

PARI

{a(n)=sum(k=0,n,binomial(n,k)*(k^2-1)^(n-k))}
for(n=0,25,print1(a(n),", "))

PARI

{a(n)=n!*polcoeff(sum(k=0,n,exp((k^2-1)*x +x*O(x^n))*x^k/k!),n)}
for(n=0,25,print1(a(n),", "))

PARI

/* From Sum_{n>=0} x^n/(1 - (n^2-1)*x)^(n+1): */
{a(n)=polcoeff(sum(k=0, n, x^k/(1-(k^2-1)*x +x*O(x^n))^(k+1)), n)}
for(n=0,25,print1(a(n),", "))

Formula

a(n) = Sum_{k=0..n} C(n,k) * (k^2-1)^(n-k).

O.g.f.: Sum_{n>=0} x^n / (1 - (n^2-1)*x)^(n+1). - Paul D. Hanna, Jul 30 2014