A190877 Expansion of e.g.f. exp(x+x^5).

1, 1, 1, 1, 1, 121, 721, 2521, 6721, 15121, 1844641, 20013841, 119845441, 519072841, 1816454641, 223394731561, 3501661887361, 29675906201761, 177923109591361, 844925253766561, 104750282797418881

Offset: 0

Author

Vladimir Kruchinin, May 23 2011

Keywords

• nonn

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..510

Crossrefs

Cf. A047974, A118395, A190875.

Programs

Mathematica

With[{nn=30},CoefficientList[Series[Exp[x+x^5],{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jan 25 2015 *)

Maxima

a(n):=n!*sum(binomial(n+(-4)*j,j)/(n+(-4)*j)!,j,0,n/4);

PARI

a(n) = if(n<5, 1, a(n-1)+5!*binomial(n-1, 4)*a(n-5)); \\ Seiichi Manyama, Feb 25 2022

Formula

a(n) = n! * Sum_{j=0..n/4} binomial(n+(-4)*j,j)/(n+(-4)*j)!.

a(n) = a(n-1) + 5! * binomial(n-1,4) * a(n-5) for n > 4. - Seiichi Manyama, Feb 25 2022