A384018 a(n) = [x^n] Product_{k=0..n-1} (1 + k*x)^3.

1, 0, 3, 63, 1767, 63690, 2822740, 148810032, 9104502015, 634448680884, 49622704133175, 4305280182748875, 410376649359397380, 42633179822414174760, 4794685285831034253660, 580373328155358031572600, 75234419898396217903091151, 10398952352945773993329785448, 1526704288048697734221906020641

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

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

Prog

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

Crossrefs

Cf. A342111, A384029.

Cf. A384026.

Sequence in context: A133275 A258657 A331012 * A386416 A391468 A369955

Adjacent sequences: A384015 A384016 A384017 * A384019 A384020 A384021

Keyword

nonn

Author

Seiichi Manyama, May 17 2025

Status

approved