A397094 Numerators of coefficients in expansion of Product_{k>=1} (1+x^k)^(k/2).

1, 1, 7, 33, 331, 1255, 7331, 23137, 528627, 1678091, 9634009, 28382599, 330241631, 950294211, 5450472475, 15571967713, 701569265347, 1972778241139, 11081264027421, 30752846697963, 341394914833541, 942115702568569, 5177065777113957, 14160495993439431, 309192824835902071

Offset

0,3

Comments

G.f. of a(n)/A046161(n) is the square root of the g.f. for A026007.

Links

Table of n, a(n) for n=0..24.

Formula

a(n) / A046161(n) ~ zeta(3)^(1/6) * exp(3^(4/3) * zeta(3)^(1/3) * n^(2/3) / 2^(5/3)) / (2^(7/8) * 3^(1/3) * sqrt(Pi) * n^(2/3)).

Example

1, 1/2, 7/8, 33/16, 331/128, 1255/256, 7331/1024, 23137/2048, 528627/32768, 1678091/65536, ...

Mathematica

nmax = 25; CoefficientList[Series[Product[(1+x^k)^(k/2), {k, 1, nmax}], {x, 0, nmax}], x] // Numerator

Crossrefs

Denominators are A046161.

Cf. A026007, A232976.

Sequence in context: A333565 A215125 A204706 * A197995 A207150 A197565

Adjacent sequences: A397090 A397091 A397092 * A397096 A397097 A397099

Keyword

nonn,frac

Author

Vaclav Kotesovec, Jun 16 2026

Status

approved