A299162 Expansion of 1/(1 - x*Product_{k>=1} 1/(1 - k*x^k)).

1, 1, 2, 6, 17, 49, 135, 380, 1051, 2925, 8119, 22548, 62574, 173767, 482360, 1339126, 3717700, 10321163, 28653557, 79548612, 220843925, 613110573, 1702128034, 4725475979, 13118945083, 36421037100, 101112695940, 280710759278, 779313926949, 2163544401343, 6006468273440

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..2256

N. J. A. Sloane, Transforms

Formula

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

a(0) = 1; a(n) = Sum_{k=1..n} A006906(k-1)*a(n-k).

Mathematica

nmax = 30; CoefficientList[Series[1/(1 - x Product[1/(1 - k x^k), {k, 1, nmax}]), {x, 0, nmax}], x]

Crossrefs

Antidiagonal sums of A297328.

Cf. A006906, A067687, A299105, A299106, A299108, A299164, A299166, A299167.

Sequence in context: A077983 A365244 A036365 * A244400 A052536 A122100

Adjacent sequences: A299159 A299160 A299161 * A299163 A299164 A299165

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 04 2018

Status

approved