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Expansion of Product_{k>=1} (1 - x^k/(1 - x)^k).
4

%I #9 Apr 03 2019 03:00:30

%S 1,-1,-2,-3,-4,-4,-1,9,34,89,200,409,779,1394,2339,3624,4974,5323,

%T 1682,-13279,-56222,-163136,-408768,-943275,-2059237,-4310179,

%U -8712425,-17072901,-32486302,-60006278,-107341413,-184979170,-303998680,-467127625,-642495990,-696247140

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

%C First differences of the binomial transform of A010815.

%C Convolution inverse of A218482.

%p a:=series(mul((1-x^k/(1-x)^k),k=1..100),x=0,35): seq(coeff(a,x,n),n=0..34); # _Paolo P. Lava_, Apr 02 2019

%t nmax = 35; CoefficientList[Series[Product[(1 - x^k/(1 - x)^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A010815, A103446, A129519, A218482, A307311.

%K sign

%O 0,3

%A _Ilya Gutkovskiy_, Apr 02 2019