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%I #10 Jan 07 2013 17:09:45
%S 1,2,7,39,314,3388,46409,776267,15406059,354928082,9330754204,
%T 276092552520,9092298247070,330151121828252,13114259187006717,
%U 566025800996830823,26391137839213285415,1322515573450223865750,70912312814053387968103,4052279260763983306587339
%N G.f.: 1/(1-x) = Sum_{n>=0} a(n)*x^n * Product_{k=1..n+1} (1-k*x).
%C Compare to: 1 = Sum_{n>=0} A082161(n)*x^n * Product_{k=1..n+1} (1-k*x).
%e 1/(1-x) = (1-x) + 2*x*(1-x)*(1-2*x) + 7*x^2*(1-x)*(1-2*x)*(1-3*x) + 39*x^3*(1-x)*(1-2*x)*(1-3*x)*(1-4*x) + 314*x^4*(1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x) + 3388*x^5*(1-x)*(1-2*x)*(1-3*x)*(1-4*x)*(1-5*x)*(1-6*x) +...
%o (PARI) {a(n)=if(n==0, 1, 1-polcoeff(sum(k=0, n-1, a(k)*x^k*prod(j=1, k+1, 1-j*x+x*O(x^n))), n))}
%o for(n=0,20,print1(a(n),", "))
%Y Cf. A082161, A118805.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jan 06 2013
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