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%I #3 Apr 14 2013 12:34:15
%S 1,1,3,19,300,11768,1193594,302611474,188884066846,288112683033594,
%T 1069431906358800731,9633610233639395592895,
%U 210208585613243673600527636,11095213297186302234251136888284,1415095855034367649056280021793496073,435753686684779400844511781608578944222819
%N G.f.: exp( Sum_{n>=1} A224678(n^2) * x^n/n ).
%C A224678 is the logarithmic derivative of A023361, where A023361(n) = number of compositions of n into positive triangular numbers.
%F Logarithmic derivative yields A224680.
%e G.f.: A(x) = 1 + x + 3*x^2 + 19*x^3 + 300*x^4 + 11768*x^5 + 1193594*x^6 +...
%e where
%e log(A(x)) = x + 5*x^2/2 + 49*x^3/3 + 1117*x^4/4 + 57181*x^5/5 + 7086833*x^6/6 +...+ A224678(n^2)*x^n/n +...
%o (PARI) {A224678(n)=n*polcoeff(-log(1-sum(r=1, sqrtint(2*n+1), x^(r*(r+1)/2)+x*O(x^n))), n)}
%o {a(n)=polcoeff(exp(sum(m=1, n, A224678(m^2)*x^m/m)+x*O(x^n)), n)}
%o for(n=0, 20, print1(a(n), ", "))
%Y Cf. A224678, A224680, A224608.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Apr 14 2013
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