A384029 a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^4.

1, 0, 6, 180, 7206, 370880, 23477380, 1768061064, 154544373158, 15387101825184, 1719596420272980, 213181689525888600, 29036623040055512332, 4310582688852993653568, 692756995680614782818992, 119830419866883597939018000, 22198322332579642585088580870, 4384714751330840129324051474880

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

a(n) = Sum_{0<=i, j, k, l<=n and i+j+k+l=3*n} |Stirling1(n,i) * Stirling1(n,j) * Stirling1(n,k) * Stirling1(n,l)|.

Prog

(PARI) a(n) = sum(i=0, n, sum(j=0, 3*n-i, sum(k=0, 3*n-i-j, abs(stirling(n, i, 1)*stirling(n, j, 1)*stirling(n, k, 1)*stirling(n, 3*n-i-j-k, 1)))));

Crossrefs

Cf. A342111, A384018.

Cf. A384027, A384030.

Cf. A384031.

Sequence in context: A368730 A381846 A135395 * A337756 A141121 A383871

Adjacent sequences: A384026 A384027 A384028 * A384030 A384031 A384032

Keyword

nonn

Author

Seiichi Manyama, May 17 2025

Status

approved