A370732 a(n) = 4^n * [x^n] Product_{k>=1} 1/(1 - 2*x^k)^(1/4).

1, 2, 18, 108, 822, 4796, 37492, 231704, 1738150, 11857004, 87262684, 617409128, 4638712124, 33724007896, 253800160808, 1894353653552, 14350905612038, 108412437326412, 827441075006796, 6308125533133896, 48388714839180756, 371391625244862600, 2860885559165073624

Offset: 0

Author

Vaclav Kotesovec, Feb 28 2024

Keywords

• nonn

Crossrefs

Cf. A070933 (m=1), A370713 (m=2), A370715 (m=3), A370733 (m=5).

Programs

Mathematica

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

Formula

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

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