A384030 a(n) = [x^(2*n)] Product_{k=0..n-1} (1 + k*x)^4.

1, 0, 1, 248, 79441, 38878520, 27741179521, 27412462941136, 35965398129639713, 60588665662486807184, 127588718827126433989569, 328596587850349392471155720, 1016488989627693108972046560497, 3720090951049096346043302894560648, 15901046580509525131539058273675597889

Offset

0,4

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = Sum_{0<=i, j, k, l<=n and i+j+k+l=2*n} |Stirling1(n,i) * Stirling1(n,j) * Stirling1(n,k) * Stirling1(n,l)|.

Prog

(PARI) a(n) = sum(i=0, n, sum(j=0, 2*n-i, sum(k=0, 2*n-i-j, abs(stirling(n, i, 1)*stirling(n, j, 1)*stirling(n, k, 1)*stirling(n, 2*n-i-j-k, 1)))));

Crossrefs

Cf. A384027, A384029.

Sequence in context: A030062 A030650 A299831 * A045254 A197349 A197400

Adjacent sequences: A384027 A384028 A384029 * A384031 A384032 A384033

Keyword

nonn

Author

Seiichi Manyama, May 17 2025

Status

approved