%I A135921
%S A135921 1,1,3,13,81,669,6955,88505,1346209,23998521,493956467,11596542533,
%T A135921 307301505073,9110471500693,299893197116059,10888674034993905,
%U A135921 433549376981078593,18833037527449398129,888439543634687700579
%N A135921 O.g.f.: A(x) = Sum_{n>=0} x^n / Product_{k=0..n} (1 - k*(k+1)*x).
%e A135921 O.g.f.: A(x) = 1 + x/(1-2x) + x^2/((1-2x)*(1-6x)) + x^3/((1-2x)*(1-6x)*(1-12x)) 
               + x^4/((1-2x)*(1-6x)*(1-12x)*(1-20x)) + ...
%e A135921 Also generated by iterated binomial transforms in the following way:
%e A135921 [1,3,13,81,669,6955,88505,...] = BINOMIAL^2([1,1,5,31,253,2673,34833,
               ..]);
%e A135921 [1,5,31,253,2673,34833,541879,...] = BINOMIAL^4([1,1,7,57,577,7389,...]);
%e A135921 [1,7,57,577,7389,115983,2151493,...] = BINOMIAL^6([1,1,9,91,1101,16497,
               ...]);
%e A135921 [1,9,91,1101,16497,301669,..] = BINOMIAL^8([1,1,11,133,1873,32061,..]);
%e A135921 [1,11,133,1873,32061,666579,...] = BINOMIAL^10([1,1,13,183,2941,56529,
               ...]);
%e A135921 etc.
%o A135921 (PARI) a(n)=polcoeff(sum(k=0, n, x^k/prod(j=0, k, 1-j*(j+1)*x+x*O(x^n))), 
               n)
%Y A135921 Cf. A135920, A124373.
%Y A135921 Sequence in context: A112935 A074514 A020014 this_sequence A005923 A089461 
               A000684
%Y A135921 Adjacent sequences: A135918 A135919 A135920 this_sequence A135922 A135923 
               A135924
%K A135921 nonn
%O A135921 0,3
%A A135921 Paul D. Hanna (pauldhanna(AT)juno.com), Dec 06 2007