A298850 Expansion of Product_{k>=1} (1 + x^(k*(k+1)/2))^(k*(k+1)/2).

1, 1, 0, 3, 3, 0, 9, 9, 0, 19, 29, 10, 33, 63, 30, 66, 156, 90, 110, 300, 235, 276, 561, 465, 558, 1083, 1065, 1154, 1877, 1983, 2295, 3834, 3879, 3861, 6858, 7452, 7561, 12613, 13252, 13057, 22161, 25569, 24582, 35985, 44193, 44970, 63495, 79105, 77143, 104046, 134820, 138759, 182511, 222600

Offset: 0

Author

Ilya Gutkovskiy, Mar 09 2018

Keywords

• nonn

Crossrefs

Cf. A000217, A024940, A027999, A028377, A291649, A298730.

Programs

Mathematica

nmax = 53; CoefficientList[Series[Product[(1 + x^(k (k + 1)/2))^(k (k + 1)/2), {k, 1, nmax}], {x, 0, nmax}], x]

Formula

G.f.: Product_{k>=1} (1 + x^A000217(k))^A000217(k).