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URL: https://oeis.org/A394200

⇱ A394200 - OEIS

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A394200
Expansion of Product_{k>=1} (1 + x^(k*(k+2))) / (1 - x^(k*(k+2))).
1
1, 0, 0, 2, 0, 0, 2, 0, 2, 2, 0, 4, 2, 0, 4, 4, 2, 4, 6, 4, 4, 6, 4, 8, 10, 4, 12, 14, 4, 12, 16, 8, 18, 18, 12, 26, 18, 12, 32, 26, 18, 36, 34, 28, 36, 36, 36, 48, 48, 40, 64, 62, 40, 72, 74, 52, 90, 82, 72, 112, 84, 84, 132, 108, 102, 148, 138, 128, 156, 154, 154
OFFSET
0,4
LINKS
FORMULA
a(n) ~ Gamma(1 + b/d) * ((4-sqrt(2))*zeta(3/2))^(2/3 + b/(3*d)) * d^(1/6 + b/(3*d)) * exp(3*Pi^(1/3) * ((4-sqrt(2))*zeta(3/2))^(2/3) * (n/d)^(1/3) / 4) / (2^(7/2 + 3*b/(2*d)) * sqrt(3) * Pi^(7/6 - b/(6*d)) * n^(7/6 + b/(3*d))), where d = 1, b = 2.
MATHEMATICA
nmax = 150; CoefficientList[Series[Product[(1 + x^(k*(k+2))) / (1 - x^(k*(k+2))), {k, 1, Floor[Sqrt[1 + nmax] + 1]}], {x, 0, nmax}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Mar 12 2026
STATUS
approved