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

0,6

Links

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

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A047974, A118395, A190875.

Sequence in context: A141350 A235408 A361703 * A361636 A354554 A367720

Adjacent sequences: A190874 A190875 A190876 * A190878 A190879 A190880

Keyword

nonn

Author

Vladimir Kruchinin, May 23 2011

Status

approved