%I A124373
%S A124373 1,1,2,6,25,135,909,7417,71698,806968,10427825,152915697,2519879761,
%T A124373 46276398129,940296067422,21007099850230,513172107841525,
%U A124373 13640345170943527,392780078386164389,12204609567437300313
%N A124373 O.g.f.: A(x) = Sum_{n>=0} x^n / Product_{k=0..n} (1 - k*(k+1)/2*x).
%F A124373 O.g.f.: A(x) = 1 + x/(1-x) + x^2/((1-x)*(1-3x)) + x^3/((1-x)*(1-3x)*(1-6x)) 
               + x^3/((1-x)*(1-3x)*(1-6x)*(1-10x)) + ...
%e A124373 Also generated by iterated binomial transforms in the following way:
%e A124373 [1,2,6,25,135,909,7417,71698,...] = BINOMIAL([1,1,3,12,64,433,3567,..]);
%e A124373 [1,3,12,64,433,3567,34905,...] = BINOMIAL^2([1,1,4,20,129,1045,...]);
%e A124373 [1,4,20,129,1045,10209,117069,...] = BINOMIAL^3([1,1,5,30,226,2121,...]);
%e A124373 [1,5,30,226,2121,23919,314605,...] = BINOMIAL^4([1,1,6,42,361,3835,...]);
%e A124373 [1,6,42,361,3835,48885,724569,...] = BINOMIAL^5([1,1,7,56,540,6385,...]);
%e A124373 [1,7,56,540,6385,90519,1490457,..] = BINOMIAL^6([1,1,8,72,769,9993,...]);
%e A124373 etc.
%p A124373 a(n)=polcoeff(sum(k=0,n,x^k/prod(j=0,k,1-j*(j+1)/2*x+x*O(x^n))),n)
%Y A124373 Sequence in context: A143917 A009326 A001258 this_sequence A010787 A008933 
               A020010
%Y A124373 Adjacent sequences: A124370 A124371 A124372 this_sequence A124374 A124375 
               A124376
%K A124373 nonn
%O A124373 0,3
%A A124373 Paul D. Hanna (pauldhanna(AT)juno.com), Oct 28 2006