A394262 Expansion of Product_{k>=1} (1 + x^(2*k^2-1)) / (1 - x^(2*k^2-1)).

1, 2, 2, 2, 2, 2, 2, 4, 6, 6, 6, 6, 6, 6, 8, 10, 10, 12, 14, 14, 14, 16, 18, 18, 22, 26, 26, 26, 28, 30, 30, 36, 42, 42, 44, 48, 50, 50, 58, 66, 66, 70, 76, 78, 78, 86, 94, 94, 102, 114, 118, 120, 130, 138, 138, 150, 168, 174, 178, 190, 198, 198, 212, 232, 238

Offset

0,2

Comments

Convolution of A291748 and A394243.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Formula

a(n) ~ ((4 - sqrt(2))*zeta(3/2))^(2/3) * exp(3*Pi^(1/3) * ((4 - sqrt(2))*zeta(3/2))^(2/3) * n^(1/3) / 2^(7/3)) / (2^(23/6) * sqrt(3) * Pi^(1/6) * sin(Pi/sqrt(2)) * n^(7/6)).

Mathematica

nmax = 150; CoefficientList[Series[Product[(1+x^(2*k^2-1))/(1-x^(2*k^2-1)), {k, 1, Sqrt[(nmax+1)/2]+1}], {x, 0, nmax}], x]

Crossrefs

Cf. A291748, A394243, A394261.

Sequence in context: A307616 A202709 A279611 * A008767 A244461 A366811

Adjacent sequences: A394259 A394260 A394261 * A394263 A394264 A394265

Keyword

nonn

Author

Vaclav Kotesovec, Mar 14 2026

Status

approved