A376628 G.f.: Sum_{k>=0} x^(k*(k+1)) / Product_{j=1..k} (1 - x^(2*j-1)).

1, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 3, 5, 5, 5, 7, 7, 8, 10, 10, 12, 14, 15, 17, 19, 21, 23, 27, 29, 31, 37, 39, 43, 49, 52, 58, 64, 70, 76, 84, 92, 99, 111, 119, 129, 143, 153, 167, 183, 197, 213, 233, 251, 271, 295, 317, 343, 372, 400, 430, 466, 500, 538, 582, 622, 670

Offset

0,7

Links

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

Formula

G.f.: Sum_{k>=0} Product_{j=1..k} x^(2*j)/(1 - x^(2*j-1)).

a(n) ~ exp(Pi*sqrt(n/6)) / (2^(5/2) * sqrt(n)).

Conjectural g.f.: (1 + q * nu(-q))/(1 + q) = 1 + Sum_{k >= 0} q^(k+2)*Product_{j = 1..k} 1 + q^(2*j+1), where nu(q) is the g.f. of A053254. - Peter Bala, Jan 03 2025

Mathematica

nmax=100; CoefficientList[Series[Sum[x^(k*(k+1))/Product[1-x^(2*j-1), {j, 1, k}], {k, 0, Sqrt[nmax]}], {x, 0, nmax}], x]

Crossrefs

Cf. A003106, A053251, A053254, A053258, A053282, A333179.

Sequence in context: A062051 A179269 A108711 * A261736 A328796 A247049

Adjacent sequences: A376625 A376626 A376627 * A376629 A376630 A376631

Keyword

nonn,easy

Author

Vaclav Kotesovec, Sep 30 2024

Status

approved