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

0,4

Links

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

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

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 *)

Prog

(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), ", "))

Crossrefs

Cf. variants: A135742, A135743, A135744, A135746, A135747.

Sequence in context: A204211 A349117 A125796 * A080895 A047899 A229041

Adjacent sequences: A135742 A135743 A135744 * A135746 A135747 A135748

Keyword

nonn

Author

Paul D. Hanna, Nov 27 2007

Status

approved