A285240 Expansion of Product_{k>=1} (1 + k*x^k)^(k^2).

1, 1, 8, 35, 115, 429, 1425, 4803, 15398, 48940, 151046, 459000, 1373219, 4037721, 11723911, 33566828, 94993571, 265722551, 735543433, 2015558930, 5471271099, 14719853084, 39266487114, 103908002173, 272855152096, 711272144097, 1841162650896, 4734074846631

Offset: 0

Author

Vaclav Kotesovec, Apr 15 2017

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..5000

Crossrefs

Cf. A022629, A027998, A266891, A285241, A285242.

Programs

Mathematica

nmax = 40; CoefficientList[Series[Product[(1 + k*x^k)^(k^2), {k,1,nmax}], {x,0,nmax}], x]
nmax = 40; s = 1 + x; Do[s*=Sum[Binomial[k^2, j]*k^j*x^(j*k), {j, 0, Floor[nmax/k] + 1}]; s = Select[Expand[s], Exponent[#, x] <= nmax &];, {k, 2, nmax}]; CoefficientList[s, x]