A384027 a(n) = [x^(3*n)] Product_{k=0..n-1} (1 + k*x)^4.

1, 0, 0, 0, 1296, 2764800, 8041766400, 34726710251520, 219045033712578816, 1956771788423009992704, 24009126017002632247173120, 393692515265172002272138690560, 8424620140673205407840209386541056, 230472036551670538296109810120063451136, 7917891968134805796965854747528387122954240

Offset

0,5

Links

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

Formula

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

Prog

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

Crossrefs

Cf. A342111, A384026.

Cf. A384029, A384030.

Sequence in context: A223360 A204083 A067492 * A222338 A013841 A358648

Adjacent sequences: A384024 A384025 A384026 * A384028 A384029 A384030

Keyword

nonn

Author

Seiichi Manyama, May 17 2025

Status

approved