A135745 E.g.f.: A(x) = Sum_{n>=0} exp((n-1)*x)^n * x^n/n!.

1, 1, 1, 7, 49, 501, 6841, 115123, 2362305, 57768553, 1646192881, 53952383871, 2010872281969, 84330050952733, 3945169959883881, 204416253047774251, 11655594262050124801, 727189793270478477777, 49395902623624761264865

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, A135744, A135746, A135747.

Programs

Mathematica

Flatten[{1, Table[Sum[Binomial[n, k]*(k*(k - 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*(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