A299167 Expansion of 1/(1 - x*Product_{k>=1} (1 + x^k)^k).

1, 1, 2, 5, 14, 36, 94, 243, 628, 1619, 4178, 10776, 27793, 71682, 184879, 476832, 1229830, 3171942, 8180989, 21100215, 54421187, 140361900, 362018270, 933709453, 2408202606, 6211182512, 16019743522, 41317765457, 106565859669, 274852289679, 708892898170, 1828360759013, 4715667307920

Offset: 0

Author

Ilya Gutkovskiy, Feb 04 2018

Keywords

• nonn

Links

• N. J. A. Sloane, Transforms

Crossrefs

Antidiagonal sums of A277938.

Cf. A026007, A067687, A299105, A299106, A299108, A299162, A299164, A299166.

Programs

Mathematica

nmax = 32; CoefficientList[Series[1/(1 - x Product[(1 + x^k)^k, {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

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

a(0) = 1; a(n) = Sum_{k=1..n} A026007(k-1)*a(n-k).