A384019 a(n) = [x^n] Product_{k=0..n-1} 1/(1 - k*x)^3.

1, 0, 6, 198, 8718, 493620, 34379705, 2848881861, 274014843102, 30021594006888, 3692052527349420, 503688013660560300, 75497500934983279207, 12333902414342152783230, 2181353542325197013657520, 415235853517370112251703000, 84651012612907530893554863870, 18400893142622338322496213279696, 4248568325843735030714223895999412

Offset

0,3

Links

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

Formula

a(n) = Sum_{i, j, k>=0 and i+j+k=n} Stirling2(i+n-1,n-1) * Stirling2(j+n-1,n-1) * Stirling2(k+n-1,n-1) for n > 0.

Prog

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

Crossrefs

Cf. A384023.

Sequence in context: A373234 A380083 A305167 * A112845 A373238 A109058

Adjacent sequences: A384016 A384017 A384018 * A384020 A384021 A384022

Keyword

nonn

Author

Seiichi Manyama, May 17 2025

Status

approved