A303651 Main diagonal of irregular triangle A303650.

1, 3, 15, 100, 840, 8589, 104104, 1463760, 23457780, 422352880, 8443603509, 185620024044, 4450814005365, 115607871091860, 3233811469903935, 96919878129098048, 3098520826729103844, 105255099799959987720, 3785952834976524485140, 143750180460098987633040, 5745630052052437089326175, 241143250707191288860686084, 10603124545177769605263358275, 487432649463606266257377179400

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..100 (terms 0..50 from Paul D. Hanna)

Formula

a(n) ~ sqrt(3) * 2^(n+2) * n! / Pi. - Vaclav Kotesovec, Feb 11 2026

Mathematica

nmax = 25; Table[SeriesCoefficient[(1-y)^2 * Sum[(2*k + 1)*y^k*(1 + x*(1-y)^2)^(k*(k+1)/2), {k, 0, n}], {x, 0, n}, {y, 0, n}], {n, 0, nmax}] (* Vaclav Kotesovec, Feb 11 2026 *)

Crossrefs

Cf. A303650, A303652.

Sequence in context: A147664 A384680 A219779 * A350954 A196962 A074521

Adjacent sequences: A303648 A303649 A303650 * A303652 A303653 A303654

Keyword

nonn

Author

Paul D. Hanna, Apr 30 2018

Status

approved