A370713 a(n) = 2^n * [x^n] Product_{k>=1} 1/(1 - 2*x^k)^(1/2).

1, 2, 10, 36, 150, 524, 2116, 7528, 29158, 107404, 409388, 1526712, 5843580, 22048056, 84476488, 322465104, 1240657798, 4769404556, 18436257820, 71280387736, 276583603220, 1074167182184, 4181581140280, 16295088132272, 63609310195164, 248542739388472, 972391744910392

Offset: 0

Author

Vaclav Kotesovec, Feb 27 2024

Keywords

• nonn

Crossrefs

Cf. A070933, A370709.

Programs

Mathematica

nmax = 35; CoefficientList[Series[Product[1/(1-2*x^k), {k, 1, nmax}]^(1/2), {x, 0, nmax}], x] * 2^Range[0, nmax]
nmax = 35; CoefficientList[Series[Product[1/(1-2*(2*x)^k), {k, 1, nmax}]^(1/2), {x, 0, nmax}], x]
nmax = 35; CoefficientList[Series[Sqrt[-1/QPochhammer[2,x]], {x, 0, nmax}], x] * 2^Range[0, nmax]

Formula

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

a(n) ~ 4^n / sqrt(Pi*QPochhammer(1/2)*n).