A370738 - OEIS

A370738

a(n) = 8^n * [x^n] Product_{k>=1} (1 + 3*x^k)^(1/4).

1, 6, -6, 1428, -13146, 280788, -3785820, 93142824, -1851272826, 37533646212, -765409050420, 16617464296728, -357906128318628, 7730398360992840, -168750405673899000, 3719099270015849040, -82288133754592611642, 1828585054153956768612, -40828782977534929747524, 915461326204911371035320

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..19.

FORMULA

G.f.: Product_{k>=1} (1 + 3*(8*x)^k)^(1/4).

a(n) ~ (-1)^(n+1) * QPochhammer(-1/3)^(1/4) * 24^n / (4 * Gamma(3/4) * n^(5/4)).

MATHEMATICA

nmax = 20; CoefficientList[Series[Product[1+3*x^k, {k, 1, nmax}]^(1/4), {x, 0, nmax}], x] * 8^Range[0, nmax]

nmax = 20; CoefficientList[Series[Product[1+3*(8*x)^k, {k, 1, nmax}]^(1/4), {x, 0, nmax}], x]

CROSSREFS