A370751 - OEIS

A370751

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

1, 6, 30, 204, 966, 5748, 29388, 169944, 886278, 5169732, 27794820, 162920616, 894445212, 5274022920, 29398573272, 174041671344, 980746798278, 5821525480164, 33071756442708, 196663513473672, 1124154722216244, 6693497121210648, 38448301937075112, 229149691659210192

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..23.

FORMULA

G.f.: Product_{k>=1} ((1 + 3*(2*x)^k)/(1 - 3*(2*x)^k))^(1/2).

a(n) ~ c * 6^n / n^(1/2), where c = (QPochhammer(-1,1/3) / (Pi * QPochhammer(1/3)))^(1/2) = 1.333660169175690343841707335109800906849893636...

MATHEMATICA

nmax = 30; CoefficientList[Series[Product[(1 + 3*x^k)/(1 - 3*x^k), {k, 1, nmax}]^(1/2), {x, 0, nmax}], x] * 2^Range[0, nmax]

nmax = 30; CoefficientList[Series[Product[(1 + 3*(2*x)^k)/(1 - 3*(2*x)^k), {k, 1, nmax}]^(1/2), {x, 0, nmax}], x]

CROSSREFS