A190729 E.g.f. exp(x+1/6*x^3+1/24*x^4)

1, 1, 1, 2, 6, 16, 46, 176, 722, 2906, 13106, 66716, 345676, 1849992, 10802156, 66543296, 418075036, 2750329276, 19145683612, 137410493656, 1012831509736, 7785886770656, 62105849642376, 507682088621632, 4271236045340056, 37171085370443576

Offset

0,4

Links

Table of n, a(n) for n=0..25.

Formula

a(n)=n!*sum(k=0..n, sum(j=floor((n-k)/3)..floor((n-k)/2), binomial(j,n-k-2*j)*binomial(k,j)*2^(-2*n+2*k+3*j)*3^(-j))/k!).

D-finite with recurrence +6*a(n) -6*a(n-1) -3*(n-1)*(n-2)*a(n-3) -(n-1)*(n-2)*(n-3)*a(n-4)=0. - R. J. Mathar, Aug 20 2021

Mathematica

With[{nn=30}, CoefficientList[Series[Exp[x+x^3/6+x^4/24], {x, 0, nn}], x] Range[ 0, nn]!] (* Harvey P. Dale, Apr 08 2018 *)

Prog

(Maxima)
a(n):=n!*sum(sum(binomial(j, n-k-2*j)*binomial(k, j)*2^(-2*n+2*k+3*j)*3^(-j), j, floor((n-k)/3), floor((n-k)/2))/k!, k, 0, n);

Crossrefs

Sequence in context: A182267 A003291 A148442 * A071726 A148443 A148444

Adjacent sequences: A190726 A190727 A190728 * A190730 A190731 A190732

Keyword

nonn

Author

Vladimir Kruchinin, May 26 2011

Status

approved