cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Programs

  • 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 *)

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

Extensions

More terms from Vaclav Kotesovec, Jun 16 2025