A258796 a(n) = [x^n] Product_{k=1..n} 1/(x^(3*k)*(1-x^k)^3).

1, 15, 882, 67385, 5938518, 575782833, 59765085601, 6529604684991, 742474127495175, 87176531917206953, 10508492822243329854, 1294860745291809207237, 162553748258042032103013, 20735748733960087597815855, 2682101373558320853655174803

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

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... .

Mathematica

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

Crossrefs

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

Sequence in context: A358802 A121292 A208304 * A232364 A264562 A211109

Adjacent sequences: A258793 A258794 A258795 * A258797 A258798 A258799

Keyword

nonn

Author

Vaclav Kotesovec, Jun 10 2015

Status

approved