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%I #13 Dec 22 2018 04:42:20
%S 1,1,3,10,40,184,948,5384,33300,222192,1587512,12071776,97206544,
%T 825343600,7362067888,68772244640,670917511424,6818719677952,
%U 72038876668544,789610228149632,8963457852609984,105211331721594368,1275095788516589952,15934546466314258688
%N G.f.: Sum_{n>=0} x^n / Product_{k=0..n} (1 - k*x)^2.
%C Compare to o.g.f. of Bell numbers: Sum_{n>=0} x^n / Product_{k=0..n} (1 - k*x).
%H Vaclav Kotesovec, <a href="/A216367/b216367.txt">Table of n, a(n) for n = 0..300</a>
%e G.f.: A(x) = 1 + x + 3*x^2 + 10*x^3 + 40*x^4 + 184*x^5 + 948*x^6 +...
%e where
%e A(x) = 1 + x/(1-x)^2 + x^2/((1-x)*(1-2*x))^2 + x^3/((1-x)*(1-2*x)*(1-3*x))^2 + x^4/((1-x)*(1-2*x)*(1-3*x)*(1-4*x))^2 +...
%t With[{nn=30},CoefficientList[Series[Sum[x^n/Product[(1-k*x)^2,{k,0,n}],{n,0,nn}],{x,0,nn}],x]] (* _Harvey P. Dale_, Dec 15 2018 *)
%o (PARI) {a(n)=polcoeff(sum(m=0, n, x^m/prod(k=1, m, 1-k*x +x*O(x^n))^2), n)}
%o for(n=0,30,print1(a(n),", "))
%Y Cf. A216373, A000110.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Sep 05 2012