A376627 G.f.: Sum_{k>=0} x^(k*(k+1)/2) * Product_{j=1..k} (1 + x^(2*j))^2.

1, 1, 0, 3, 0, 3, 1, 3, 2, 4, 4, 3, 8, 2, 10, 2, 14, 2, 19, 3, 20, 7, 23, 11, 26, 17, 25, 26, 27, 35, 29, 48, 27, 64, 28, 81, 30, 98, 32, 119, 37, 139, 47, 159, 59, 183, 77, 199, 105, 217, 137, 237, 180, 251, 232, 266, 292, 281, 364, 293, 447, 309, 540, 331, 645, 350

Offset

0,4

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))^2 * x^j.

a(n) ~ c * A376659^sqrt(n) / sqrt(n), where c = sqrt(5/168 + sqrt(11/23) * cosh(arccosh(17*sqrt(23)/(2*11^(3/2)))/3)/21) = 0.2512284115765342169430117...

Mathematica

nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1)/2)*Product[1+x^(2*j), {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 + x^(2*k))*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. A179049, A376631, A376659.

Sequence in context: A318504 A343877 A318505 * A237595 A322575 A166445

Adjacent sequences: A376624 A376625 A376626 * A376628 A376629 A376630

Keyword

nonn

Author

Vaclav Kotesovec, Sep 30 2024

Status

approved