A370715 - OEIS

A370715

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

1, 6, 126, 1818, 32130, 452142, 8006526, 117619290, 1999520154, 31550881374, 527781570174, 8556328428786, 145177242834330, 2404855490356782, 40907085509085750, 691705559193384114, 11840743106503713594, 202344257179543757526, 3487245860820904368822, 60077736592697832105330

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OFFSET

0,2

LINKS

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

FORMULA

G.f.: Product_{k>=1} 1/(1 - 2*(9*x)^k)^(1/3).

a(n) ~ c * 18^n / n^(2/3), where c = 1 / (Gamma(1/3) * QPochhammer(1/2)^(1/3)) = 0.564734286036917647642848904946237...

MATHEMATICA

nmax = 25; CoefficientList[Series[Product[1/(1-2*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax]

nmax = 25; CoefficientList[Series[Product[1/(1-2*(9*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x]

nmax = 25; CoefficientList[Series[(-1/QPochhammer[2, x])^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax]

CROSSREFS

Cf. A070933, A370716.

Sequence in context: A268685 A109820 A228290 * A004993 A237428 A255900

Adjacent sequences: A370712 A370713 A370714 * A370716 A370717 A370718

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Feb 27 2024

STATUS

approved