A376623 - OEIS

A376623

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

1, 0, 1, 2, 1, 0, 1, 2, 1, 2, 4, 2, 2, 4, 2, 2, 4, 4, 5, 4, 6, 10, 6, 6, 9, 8, 9, 8, 10, 12, 11, 14, 14, 16, 17, 18, 23, 20, 22, 26, 26, 26, 27, 34, 31, 32, 39, 40, 43, 42, 48, 54, 55, 56, 63, 72, 68, 74, 80, 84, 88, 90, 101, 104, 109, 112, 121, 130, 132, 144, 152, 160

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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} (x^j + x^(3*j-1))^2.

a(n) ~ c * A376621^sqrt(n) / sqrt(n), where c = sqrt(sinh(arcsinh(3*sqrt(93)/2)/3)) / (sqrt(2)*93^(1/4)) = 0.26678318911398751342...

MATHEMATICA

nmax = 100; CoefficientList[Series[Sum[x^(k*(k+1))*Product[1+x^(2*j-1), {j, 1, k}]^2, {k, 0, Sqrt[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^(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. A376542, A376580, A376621, A376626, A376629.

Sequence in context: A076092 A080468 A321863 * A294599 A376615 A335511

Adjacent sequences: A376620 A376621 A376622 * A376624 A376625 A376626

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 30 2024

STATUS

approved