A135744 E.g.f.: A(x) = Sum_{n>=0} exp( n*(n+1)*x ) * x^n/n!.

1, 1, 5, 31, 297, 3781, 60373, 1188699, 28003825, 772499593, 24613769061, 894386029879, 36653691106585, 1679283513161229, 85360981759418485, 4781873479864452211, 293487961919565420897, 19633825959679051986961

Offset: 0

Author

Paul D. Hanna, Nov 27 2007

Keywords

• nonn

Links

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

Crossrefs

Cf. variants: A135742, A135743, A135745, A135746, A135747.

Programs

Mathematica

Flatten[{1, Table[Sum[Binomial[n, k]*(2*Binomial[k + 1, 2])^(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*(k+1))^(n-k))}
for(n=0,25,print1(a(n),", "))

PARI

{a(n)=n!*polcoeff(sum(k=0,n,exp(k*(k+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*(n+1)*x)^(n+1): */
{a(n)=polcoeff(sum(k=0, n, x^k/(1-k*(k+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*(k+1) )^(n-k).

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