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a(n) = [x^n] Product_{k=1..n} 1/(x^(3*k)*(1-x^k)^3).
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%I #5 Jun 11 2015 06:24:27

%S 1,15,882,67385,5938518,575782833,59765085601,6529604684991,

%T 742474127495175,87176531917206953,10508492822243329854,

%U 1294860745291809207237,162553748258042032103013,20735748733960087597815855,2682101373558320853655174803

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

%F a(n) ~ c * d^n / n^3, where d = 157.540286488430979726276374519534734829527107090287337321136938826336... = r^6/(r-1)^3, where r is the root of the equation polylog(2, 1-r) + log(r)^2 = 0, c = 1.797864597437050667... .

%t Table[SeriesCoefficient[1/Product[x^(3*k)*(1-x^k)^3, {k, 1, n}], {x, 0, n}], {n, 0, 20}]

%t Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}]^3, {x, 0, n*(3*n+5)/2}], {n, 0, 20}]

%Y Cf. A258788, A258790, A258792, A258794, A258795.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jun 10 2015