A370761 Expansion of Product_{k>=1} (1 + 2^(k+1)*x^k) * (1 + 2^(k-1)*x^k).

1, 5, 14, 70, 196, 640, 2248, 6480, 19072, 56000, 169792, 466560, 1327104, 3642880, 10030080, 27776000, 74541056, 199065600, 531505152, 1401405440, 3672801280, 9674588160, 25018564608, 64701071360, 166363136000, 426159636480, 1084287352832, 2756737761280, 6979072294912

Offset

0,2

Links

Table of n, a(n) for n=0..28.

Formula

a(n) ~ (Pi^2/3 + log(2)^2)^(1/4) * 2^(n - 3/4) * exp(sqrt(2*(Pi^2/3 + log(2)^2)*n)) / (3*sqrt(Pi)*n^(3/4)).

Mathematica

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

Crossrefs

Cf. A032302, A304961, A370016, A370764, A370765, A370792.

Sequence in context: A197901 A202764 A197876 * A305017 A007838 A306751

Adjacent sequences: A370758 A370759 A370760 * A370762 A370763 A370764

Keyword

nonn

Author

Vaclav Kotesovec, Mar 01 2024

Status

approved