A370749 a(n) = 2^n * [x^n] Product_{k>=1} ((1 + 2*x^k)/(1 - 2*x^k))^(1/4).

1, 2, 6, 28, 70, 300, 892, 3544, 9990, 43340, 127988, 546120, 1651356, 7227896, 22414008, 99344944, 312879302, 1396285452, 4486205892, 20057934312, 65293087284, 292353604136, 963327294536, 4308913730256, 14340603113372, 64059675491512, 215075154021384, 958968160741328

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

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

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

Mathematica

nmax = 30; CoefficientList[Series[Product[(1 + 2*x^k)/(1 - 2*x^k), {k, 1, nmax}]^(1/4), {x, 0, nmax}], x] * 2^Range[0, nmax]
nmax = 30; CoefficientList[Series[Product[(1 + 2*(2*x)^k)/(1 - 2*(2*x)^k), {k, 1, nmax}]^(1/4), {x, 0, nmax}], x]

Crossrefs

Cf. A261584, A303346, A370750.

Cf. A032302, A070933.

Cf. A370736, A370732.

Sequence in context: A074925 A141136 A115156 * A185072 A322507 A340471

Adjacent sequences: A370746 A370747 A370748 * A370750 A370751 A370752

Keyword

nonn

Author

Vaclav Kotesovec, Feb 29 2024

Status

approved