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URL: https://oeis.org/A281790

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A281790
Expansion of Product_{k>=1} (1+x^(k^2))^k.
7
1, 1, 0, 0, 2, 2, 0, 0, 1, 4, 3, 0, 0, 6, 6, 0, 4, 7, 6, 3, 8, 8, 6, 6, 4, 21, 20, 4, 1, 34, 34, 2, 8, 23, 44, 28, 19, 18, 54, 54, 18, 56, 65, 46, 25, 100, 94, 38, 42, 85, 169, 107, 56, 69, 226, 194, 62, 111, 194, 241, 125, 215, 246, 258, 207, 283, 437, 292
OFFSET
0,5
LINKS
FORMULA
a(n) ~ exp(sqrt(n/6)*Pi) / (2^(11/6) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 15 2017
MATHEMATICA
nmax = 100; CoefficientList[Series[Product[(1+x^(k^2))^k, {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 100; s = 1 + x; Do[s*=Sum[Binomial[k, j]*x^(j*k^2), {j, 0, Floor[nmax/k^2] + 1}]; s = Select[Expand[s], Exponent[#, x] <= nmax &]; , {k, 2, nmax}]; CoefficientList[s, x]
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Apr 14 2017
STATUS
approved