A285242 Expansion of Product_{k>=1} (1 + k*x^(k^2))^k.

1, 1, 0, 0, 4, 4, 0, 0, 4, 13, 9, 0, 0, 36, 36, 0, 16, 52, 63, 27, 64, 64, 108, 108, 64, 233, 277, 135, 27, 676, 676, 108, 204, 772, 1333, 765, 528, 420, 2628, 2628, 528, 1792, 3892, 3735, 1251, 5524, 5380, 4428, 4684, 6657, 12843, 10870, 6703, 3767, 28232

Offset

0,5

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Mathematica

nmax = 100; CoefficientList[Series[Product[(1 + k*x^(k^2))^k, {k, 1, nmax}], {x, 0, nmax}], x]
nmax = 100; s = 1 + x; Do[s *= Sum[Binomial[k, j]*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]

Crossrefs

Cf. A022629, A266891, A281790, A285240, A285243, A285244.

Sequence in context: A290696 A200515 A200505 * A143266 A133845 A282289

Adjacent sequences: A285239 A285240 A285241 * A285243 A285244 A285245

Keyword

nonn

Author

Vaclav Kotesovec, Apr 15 2017

Status

approved