A370750 a(n) = 9^n * [x^n] Product_{k>=1} ((1 + 2*x^k)/(1 - 2*x^k))^(1/3).

1, 12, 180, 3852, 50436, 947052, 14087844, 245858652, 3531115620, 64019229660, 950199749748, 16959724619004, 256888616329044, 4642974930688812, 71716402072904724, 1308491345357401068, 20501966472318764388, 376230182366985289164, 5987314157007778195716, 110286515004790197907836

Offset

0,2

Links

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

Formula

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

a(n) ~ QPochhammer(-1, 1/2)^(1/3) * 18^n / (Gamma(1/3) * QPochhammer(1/2)^(1/3) * n^(2/3)).

Mathematica

nmax = 20; CoefficientList[Series[Product[(1 + 2*x^k)/(1 - 2*x^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x] * 9^Range[0, nmax]
nmax = 20; CoefficientList[Series[Product[(1 + 2*(9*x)^k)/(1 - 2*(9*x)^k), {k, 1, nmax}]^(1/3), {x, 0, nmax}], x]

Crossrefs

Cf. A261584, A303346, A370749.

Cf. A032302, A070933.

Cf. A370716, A370715.

Sequence in context: A318245 A051609 A001814 * A327079 A013924 A145560

Adjacent sequences: A370746 A370748 A370749 * A370751 A370752 A370754

Keyword

nonn

Author

Vaclav Kotesovec, Feb 29 2024

Status

approved