A258798 a(n) = [x^n] Product_{k=1..n} (1+x^k)^3 / x^k.

1, 3, 12, 62, 327, 1851, 10802, 64440, 391218, 2408001, 14989608, 94197594, 596756374, 3807010920, 24435261432, 157681777148, 1022391454116, 6657413851086, 43517229086467, 285447137446989, 1878287880309900, 12395149957521672, 82014499806039711

Offset: 0

Author

Vaclav Kotesovec, Jun 10 2015

Keywords

• nonn

Crossrefs

Cf. A258797, A258799.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1+x^k)^3/x^k, {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[Product[1+x^k, {k, 1, n}]^3, {x, 0, n*(n+3)/2}], {n, 0, 30}]
(* A program to compute the constant d *) (1+r)^3/r^2 /.FindRoot[-Pi^2/12 - Log[r]^2/3 + 1/2*Log[1+r]^2 + PolyLog[2,1/(1+r)] == 0, {r, E}, WorkingPrecision->100]

Formula

a(n) ~ c * d^n / n^(3/2), where d = 7.036711302278424796297167109247361745558645910729132828752853658917..., c = 2.3254811458... .