A035295 Expansion of sum ( q^n / product( 1-q^k, k=1..3*n), n=0..inf ).

1, 1, 2, 4, 7, 11, 17, 26, 38, 54, 77, 107, 148, 201, 272, 363, 483, 635, 832, 1081, 1399, 1796, 2299, 2924, 3707, 4673, 5874, 7348, 9166, 11384, 14102, 17404, 21425, 26285, 32172, 39259, 47799, 58036, 70318, 84985, 102507, 123354, 148163, 177582, 212464, 253692, 302411

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Formula

a(n) ~ Gamma(1/3) * exp(Pi*sqrt(2*n/3)) / (2^(5/3) * 3^(7/6) * Pi^(2/3) * n^(2/3)). - Vaclav Kotesovec, Jun 16 2025

Mathematica

nmax = 50; CoefficientList[Series[Sum[x^k/Product[1 - x^j, {j, 1, 3*k}], {k, 0, nmax}], {x, 0, nmax}], x]  (* Vaclav Kotesovec, Jun 16 2025 *)
nmax = 50; p=1; s=1; Do[p=Expand[p*(1-x^(3*k))*(1-x^(3*k-1))*(1-x^(3*k-2))]; p=Take[p, Min[nmax+1, Exponent[p, x]+1, Length[p]]]; s+=x^k/p; , {k, 1, nmax}]; CoefficientList[Series[s, {x, 0, nmax}], x] (* Vaclav Kotesovec, Jun 16 2025 *)

Crossrefs

Cf. A363066, A385067.

Sequence in context: A280962 A096967 A117276 * A289010 A006999 A005252

Adjacent sequences: A035292 A035293 A035294 * A035296 A035297 A035298

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Vaclav Kotesovec, Jun 16 2025

Status

approved