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%I #9 Apr 03 2019 09:04:02
%S 1,2,5,15,44,126,357,1003,2783,7618,20627,55421,148021,393140,1038123,
%T 2724992,7112022,18465708,47726767,122861732,315123476,805428727,
%U 2051556778,5207982062,13177117709,33235023381,83574705456,209576713721,524181331710,1307849984089,3255539133109
%N Expansion of (1/(1 - x)) * Product_{k>=1} (1 + k*x^k/(1 - x)^k).
%C Binomial transform of A022629.
%F a(n) = Sum_{k=0..n} binomial(n,k)*A022629(k).
%p a:=series((1/(1-x))*mul(1+k*x^k/(1-x)^k,k=1..100),x=0,31): seq(coeff(a,x,n),n=0..30); # _Paolo P. Lava_, Apr 03 2019
%t nmax = 30; CoefficientList[Series[1/(1 - x) Product[(1 + k x^k/(1 - x)^k), {k, 1, nmax}], {x, 0, nmax}], x]
%Y Cf. A022629, A266232, A294502, A307260, A318127.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, Apr 01 2019