A306911 Expansion of Sum_{k>=0} x^(k^2) * Product_{j=1..k} (1 + x^j)^j.

1, 1, 1, 0, 1, 1, 2, 2, 1, 2, 1, 2, 5, 4, 7, 9, 7, 10, 9, 9, 13, 13, 18, 27, 31, 42, 53, 61, 71, 83, 95, 98, 115, 131, 147, 176, 207, 258, 313, 395, 481, 581, 721, 848, 1014, 1179, 1367, 1586, 1804, 2064, 2338, 2698, 3083, 3559, 4142, 4819, 5732, 6768, 8036, 9582, 11426

Offset: 0

Author

Ilya Gutkovskiy, Mar 16 2019

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..4000

Crossrefs

Cf. A306708, A306734, A318771.

Programs

Maple

N:= 100:
S:= series(add(x^(k^2)*mul((1+x^j)^j,j=1..min(k,N-k^2)),k=0..floor(sqrt(N))), x, N+1):
seq(coeff(S,x,n),n=0..N); # Robert Israel, Apr 10 2019

Mathematica

nmax = 60; CoefficientList[Series[Sum[x^(k^2) Product[(1 + x^j)^j, {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]