A281790 Expansion of Product_{k>=1} (1+x^(k^2))^k.

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

Author

Vaclav Kotesovec, Apr 14 2017

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..20000

Crossrefs

Cf. A000219, A026007, A027998, A033461, A255528, A266891, A284896, A285047.

Programs

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]

Formula

a(n) ~ exp(sqrt(n/6)*Pi) / (2^(11/6) * 3^(1/4) * n^(3/4)). - Vaclav Kotesovec, Apr 15 2017