A384023 a(n) = [x^(2*n)] Product_{k=0..n-1} 1/(1 - k*x)^3.

1, 0, 15, 6562, 5011791, 6200184825, 11429262789510, 29485293941863746, 101592807373290699207, 451093709664199690854238, 2509724586752840748604036752, 17105620782434790456521322932280, 140205097075941134305471628610608762, 1360788914644085139603907391284501566930

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

a(n) = Sum_{i, j, k>=0 and i+j+k=2*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, 2*n, sum(j=0, 2*n-i, stirling(i+n-1, n-1, 2)*stirling(j+n-1, n-1, 2)*stirling(3*n-1-i-j, n-1, 2))));

Crossrefs

Cf. A384019.

Sequence in context: A204677 A198250 A066968 * A113795 A205155 A208095

Adjacent sequences: A384020 A384021 A384022 * A384024 A384025 A384026

Keyword

nonn

Author

Seiichi Manyama, May 17 2025

Status

approved