A135742 E.g.f.: A(x) = Sum_{n>=0} exp( n*(n-1)/2 * x ) * x^n / n!.

1, 1, 1, 4, 19, 131, 1156, 12622, 166825, 2600677, 47038456, 974165336, 22829939089, 599668759483, 17512623094240, 564613124026876, 19972670155565761, 771019774737952313, 32326390781950804048

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: A135743, A135744, A135745, A135746.

Programs

Mathematica

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

PARI

{a(n)=n!*polcoeff(sum(k=0,n,exp(k*(k-1)/2*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)/2*x)^(n+1): */
{a(n)=polcoeff(sum(k=0, n, x^k/(1-k*(k-1)/2*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)/2 )^(n-k).

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