A190875 E.g.f. exp(x+x^4).

1, 1, 1, 1, 25, 121, 361, 841, 21841, 184465, 912241, 3334321, 89824681, 1063799881, 7325422105, 36454050361, 1017339566881, 15314809967521, 134865698721121, 848781820990945, 24508030788375481, 443521231499750041, 4748434334677932361

Offset: 0

Author

Vladimir Kruchinin, May 22 2011

Keywords

• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..105

Programs

Mathematica

CoefficientList[Series[E^(x+x^4), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 26 2013 *)

Maxima

a(n):=n!*sum(binomial(n-3*j,j)/(n-3*j)!,j,0,n/3);

PARI

Vec(serlaplace(exp(x+x^4+O(x^66)))) /* Joerg Arndt, May 24 2011 */

Formula

a(n)=n!*sum(j=0..n/3, binomial(n-3*j,j)/(n-3*j)!)

Recurrence: a(n) = a(n-1) + 4*(n-3)*(n-2)*(n-1)*a(n-4). - Vaclav Kotesovec, Jun 26 2013

a(n) ~ 2^(n/2-1)*exp(n^(1/4)/sqrt(2)-3*n/4)*n^(3*n/4). - Vaclav Kotesovec, Jun 26 2013