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%I #5 Jun 11 2015 06:24:07
%S 1,3,12,62,327,1851,10802,64440,391218,2408001,14989608,94197594,
%T 596756374,3807010920,24435261432,157681777148,1022391454116,
%U 6657413851086,43517229086467,285447137446989,1878287880309900,12395149957521672,82014499806039711
%N a(n) = [x^n] Product_{k=1..n} (1+x^k)^3 / x^k.
%F a(n) ~ c * d^n / n^(3/2), where d = 7.036711302278424796297167109247361745558645910729132828752853658917..., c = 2.3254811458... .
%t Table[SeriesCoefficient[Product[(1+x^k)^3/x^k, {k, 1, n}], {x, 0, n}], {n, 0, 30}]
%t Table[SeriesCoefficient[Product[1+x^k, {k, 1, n}]^3, {x, 0, n*(n+3)/2}], {n, 0, 30}]
%t (* 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]
%Y Cf. A258797, A258799.
%K nonn
%O 0,2
%A _Vaclav Kotesovec_, Jun 10 2015