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

Offset: 0

Author

Vaclav Kotesovec, Feb 28 2024

Keywords

• sign

Crossrefs

Cf. A032308 (m=1), A370711 (m=2), A370712 (m=3), A370739 (m=5).

Programs

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]

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)).