A318246 a(n) = [x^n] Product_{k>=1} (1 + 3^n*x^k).

1, 3, 9, 756, 6642, 118341, 388484100, 10474704297, 564988219686, 22878342156600, 12158489037532504050, 984798697643349485688, 159533936817604246934415, 19383278088136495245171156, 2616739259326831261950662430, 608267042060342812170824926328855679

Offset: 0

Author

Vaclav Kotesovec, Aug 22 2018

Keywords

• nonn

Comments

Conjecture: In general, if m > 1 and a(n) = [x^n] Product_{k>=1} (1 + m^n * x^k), then log(a(n)) ~ log(m)*(sqrt(2)*n^(3/2) - n/2).

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..135

Crossrefs

Cf. A292414.

Programs

Mathematica

nmax = 20; Table[SeriesCoefficient[Product[(1+3^n*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]

Formula

Conjecture: log(a(n)) ~ log(3)*sqrt(2)*n^(3/2).