A370736 a(n) = 4^n * [x^n] Product_{k>=1} (1 + 2*x^k)^(1/4).

1, 2, 2, 76, -106, 1788, -1516, 57176, -276634, 2270444, -10094212, 97699752, -664173444, 4819718488, -33236872088, 259931360688, -1894783205754, 13983087008588, -103270227527444, 779496572387208, -5855545477963244, 44016069418771976, -331519650617078376, 2514477954420678352

Offset: 0

Author

Vaclav Kotesovec, Feb 28 2024

Keywords

• sign

Crossrefs

Cf. A032302 (m=1), A370709 (m=2), A370716 (m=3), A370737 (m=5).

Programs

Mathematica

nmax = 25; CoefficientList[Series[Product[1+2*x^k, {k, 1, nmax}]^(1/4), {x, 0, nmax}], x] * 4^Range[0, nmax]
nmax = 25; CoefficientList[Series[Product[1+2*(4*x)^k, {k, 1, nmax}]^(1/4), {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} (1 + 2*(4*x)^k)^(1/4).

a(n) ~ (-1)^(n+1) * QPochhammer(-1/2)^(1/4) * 8^n / (4 * Gamma(3/4) * n^(5/4)).