%I #8 Mar 15 2018 15:33:20

%S 1,1,2,6,17,49,135,380,1051,2925,8119,22548,62574,173767,482360,

%T 1339126,3717700,10321163,28653557,79548612,220843925,613110573,

%U 1702128034,4725475979,13118945083,36421037100,101112695940,280710759278,779313926949,2163544401343,6006468273440

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

%H Alois P. Heinz, <a href="/A299162/b299162.txt">Table of n, a(n) for n = 0..2256</a>

%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>

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

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

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

%Y Antidiagonal sums of A297328.

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

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Feb 04 2018