A376626 - OEIS

A376626

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

1, 1, 2, 2, 2, 1, 3, 6, 3, 3, 7, 7, 6, 6, 9, 13, 12, 11, 16, 18, 17, 20, 22, 26, 28, 31, 36, 36, 42, 46, 50, 57, 61, 69, 72, 75, 87, 97, 100, 108, 126, 136, 141, 151, 167, 188, 195, 207, 233, 254, 265, 279, 315, 339, 355, 380, 417, 455, 473, 503, 551, 600, 627, 667, 730

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

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

FORMULA

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

a(n) ~ c * A376659^sqrt(n) / sqrt(n), where c = sqrt(1/14 + sinh(arcsinh(75*sqrt(69)/2)/3)/(7*sqrt(69))) = 0.3792934340515155206194952273079851598271882968396...

MATHEMATICA

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

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

CROSSREFS

Cf. A376580, A376623, A376630, A376659.

Sequence in context: A089258 A004065 A127496 * A350189 A289778 A277523

Adjacent sequences: A376623 A376624 A376625 * A376627 A376628 A376629

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 30 2024

STATUS

approved