Search: id:A135920
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%I A135920
%S A135920 1,1,2,7,37,264,2433,27913,386906,6346119,121159373,2655174768,
%T A135920 66028903633,1845579100993,57506847262162,1983312152411351,
%U A135920 75238783332550789,3122408658986242072,141063757638078429489
%N A135920 O.g.f.: A(x) = Sum_{n>=0} x^n / Product_{k=0..n} (1 - k^2*x).
%e A135920 O.g.f.: A(x) = 1 + x/(1-x) + x^2/((1-x)*(1-4x)) + x^3/((1-x)*(1-4x)*(1-9x))
%e A135920 + x^4/((1-x)*(1-4x)*(1-9x)*(1-16x)) + ...
%e A135920 Also generated by iterated binomial transforms in the following way:
%e A135920 [1,2,7,37,264,2433,27913,...] = BINOMIAL([1,1,4,21,151,1422,16629,..]);
%e A135920 [1,4,21,151,1422,16629,234529,...] = BINOMIAL^3([1,1,6,43,393,4596,...]);
%e A135920 [1,6,43,393,4596,66049,1125905,...] = BINOMIAL^5([1,1,8,73,811,11274,
               ...]);
%e A135920 [1,8,73,811,11274,191685,...] = BINOMIAL^7([1,1,10,111,1453,23328,...]);
%e A135920 [1,10,111,1453,23328,456033,...] = BINOMIAL^9([1,1,12,157,2367,43014,
               ...]);
%e A135920 etc.
%o A135920 (PARI) a(n)=polcoeff(sum(k=0, n, x^k/prod(j=0, k, 1-j^2*x+x*O(x^n))), 
               n)
%Y A135920 Cf. A135921, A124373.
%Y A135920 Sequence in context: A135164 A072597 A125515 this_sequence A001515 A144301 
               A083659
%Y A135920 Adjacent sequences: A135917 A135918 A135919 this_sequence A135921 A135922 
               A135923
%K A135920 nonn
%O A135920 0,3
%A A135920 Paul D. Hanna (pauldhanna(AT)juno.com), Dec 06 2007

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