A258799 a(n) = [x^n] Product_{k=1..n} (1+x^k)^3 / x^(2*k).

1, 1, 3, 13, 61, 324, 1800, 10340, 60969, 366486, 2237120, 13829487, 86394782, 544547651, 3458637273, 22113504345, 142212705879, 919294844898, 5969839457411, 38927450022860, 254776529381625, 1673102335692514, 11020847332241873, 72798664086854460

Offset: 0

Author

Vaclav Kotesovec, Jun 10 2015

Keywords

• nonn

Crossrefs

Cf. A258797, A258798.

Programs

Mathematica

Table[SeriesCoefficient[Product[(1+x^k)^3/x^(2*k), {k, 1, n}], {x, 0, n}], {n, 0, 30}]
Table[SeriesCoefficient[Product[1+x^k, {k, 1, n}]^3, {x, 0, n*(n+2)}], {n, 0, 30}]
(* A program to compute the constant d *) (1+r)^3/r /.FindRoot[Log[1+r]/Log[r] + (PolyLog[2,-r] + Pi^2/12) / Log[r]^2 == 1/6, {r, E}, WorkingPrecision->100]

Formula

a(n) ~ c * d^n / n^(3/2), where d = 7.036711302278424796297167109247361745558645910729132828752853658917..., c = 0.282321145891... .