A224681 G.f.: exp( Sum_{n>=1} A224678(n^2) * x^n/n ).

1, 1, 3, 19, 300, 11768, 1193594, 302611474, 188884066846, 288112683033594, 1069431906358800731, 9633610233639395592895, 210208585613243673600527636, 11095213297186302234251136888284, 1415095855034367649056280021793496073, 435753686684779400844511781608578944222819

Offset: 0

Author

Paul D. Hanna, Apr 14 2013

Keywords

• nonn

Comments

A224678 is the logarithmic derivative of A023361, where A023361(n) = number of compositions of n into positive triangular numbers.

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 19*x^3 + 300*x^4 + 11768*x^5 + 1193594*x^6 +...
where
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 +...
		

Crossrefs

Cf. A224678, A224680, A224608.

Programs

PARI

{A224678(n)=n*polcoeff(-log(1-sum(r=1, sqrtint(2*n+1), x^(r*(r+1)/2)+x*O(x^n))), n)}
{a(n)=polcoeff(exp(sum(m=1, n, A224678(m^2)*x^m/m)+x*O(x^n)), n)}
for(n=0, 20, print1(a(n), ", "))

Formula

Logarithmic derivative yields A224680.