A299164 Expansion of 1/(1 - x*Product_{k>=1} (1 + k*x^k)).

1, 1, 2, 5, 14, 35, 91, 233, 597, 1517, 3885, 9922, 25333, 64683, 165181, 421828, 1077277, 2750993, 7025168, 17940298, 45814165, 116996152, 298774246, 762982615, 1948434235, 4975732669, 12706571546, 32448880807, 82864981016, 211613009498, 540397935771, 1380018797044, 3524165721799

Offset: 0

Author

Ilya Gutkovskiy, Feb 04 2018

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• N. J. A. Sloane, Transforms

Crossrefs

Antidiagonal sums of A297321.

Cf. A022629, A067687, A299105, A299106, A299108, A299162, A299166, A299167.

Programs

Mathematica

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

Formula

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

a(0) = 1; a(n) = Sum_{k=1..n} A022629(k-1)*a(n-k).