A376629 G.f.: Sum_{k>=0} x^(k*(k+1)) * Product_{j=1..k} (1 + x^(2*j-1)).

1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 2, 2, 0, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 1, 3, 3, 1, 3, 3, 3, 2, 2, 3, 3, 3, 2, 4, 3, 3, 4, 3, 4, 3, 4, 4, 4, 4, 4, 5, 4, 5, 5, 5, 4, 6, 6, 4, 6, 5, 7, 6, 5, 7, 7, 6, 6, 8, 7, 7, 7, 9, 8

Offset

0,21

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) + x^(4*j-1)).

a(n) ~ exp(Pi*sqrt(n/30)) / (2*5^(1/4)*sqrt(n)).

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]
nmax = 100; p = 1; s = 1; Do[p = Expand[p*(1 + x^(2*k - 1))*x^(2*k)]; p = Take[p, Min[nmax + 1, Exponent[p, x] + 1, Length[p]]]; s += p; , {k, 1, Sqrt[nmax]}]; Take[CoefficientList[s, x], nmax + 1]

Crossrefs

Cf. A003106, A053251, A053258, A333179, A376630.

Sequence in context: A124407 A294624 A290531 * A206442 A137581 A156311

Adjacent sequences: A376626 A376627 A376628 * A376630 A376631 A376632

Keyword

nonn

Author

Vaclav Kotesovec, Sep 30 2024

Status

approved