login
Expansion of 1/(1 - x*Product_{k>=1} (1 - x^k)).
17

%I #9 Jan 18 2020 11:33:37

%S 1,1,0,-2,-3,-1,5,10,7,-9,-29,-30,10,77,108,22,-184,-351,-207,372,

%T 1041,969,-516,-2835,-3655,-284,6990,12190,5977,-14957,-37044,-30994,

%U 24144,103374,122409,-7715,-262704,-420585,-162274,589068,1309674,972747,-1057935,-3742955

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

%H Seiichi Manyama, <a href="/A299105/b299105.txt">Table of n, a(n) for n = 0..5000</a>

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

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

%F a(0) = 1; a(n) = Sum_{k=1..n} A010815(k-1)*a(n-k).

%t nmax = 43; CoefficientList[Series[1/(1 - x Product[1 - x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

%t nmax = 43; CoefficientList[Series[1/(1 - x QPochhammer[x, x]), {x, 0, nmax}], x]

%Y Antidiagonal sums of A286354.

%Y Cf. similar sequences: A067687, A299106, A299208, A302017, A318581, A318582, A331484.

%Y Cf. A010815, A299108.

%K sign

%O 0,4

%A _Ilya Gutkovskiy_, Feb 02 2018