A384087 a(n) = [x^n] Product_{k=1..n} ((1 + k*x)/(1 - k*x))^3.

1, 6, 162, 7848, 552000, 51035310, 5853933666, 802178739936, 127879052859648, 23252775004089990, 4750089647035004250, 1077069265550569663416, 268437124701985949614944, 72940650531961450912140558, 21461129870889481564510048050, 6797577340761206051865208521600, 2306127185536355501260494657447936

Offset: 0

Author

Vaclav Kotesovec, May 19 2025

Keywords

• nonn

Crossrefs

Cf. A384012, A383862.

Cf. A350366, A384086, A384088, A351764.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1+k*x)^3/(1-k*x)^3, {k, 1, n}], {x, 0, n}], {n, 0, 16}]

Formula

a(n) ~ c * d^n * n! / n, where d = 22.56625698335414867480351407039325848948214595770919713967057... and c = 0.403760467212667768540403611728406212428403946576093482938996...