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 A299164 Expansion of 1/(1 - x*Product_{k>=1} (1 + k*x^k)). 10

%I

%S 1,1,2,5,14,35,91,233,597,1517,3885,9922,25333,64683,165181,421828,

%T 1077277,2750993,7025168,17940298,45814165,116996152,298774246,

%U 762982615,1948434235,4975732669,12706571546,32448880807,82864981016,211613009498,540397935771,1380018797044,3524165721799

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

%H Alois P. Heinz, <a href="/A299164/b299164.txt">Table of n, a(n) for n = 0..1000</a>

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

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

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

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

%Y Antidiagonal sums of A297321.

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

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Feb 04 2018

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Last modified November 12 19:19 EST 2018. Contains 317116 sequences. (Running on oeis4.)