A224608 G.f.: exp( Sum_{n>=1} A219331(n^2)*x^n/n ).

1, 1, 3, 12, 81, 1335, 49309, 3882180, 633703214, 212061201327, 144669917959584, 200541263416077021, 563631413420071614333, 3206926569346230863485855, 36897315109526505791310840932, 857701705296285206387609947414980, 40254707002970300021370965171570478599

Offset: 0

Author

Paul D. Hanna, Apr 12 2013

Keywords

• nonn

Comments

A219331 is the logarithmic derivative of A006456, where A006456(n) is the number of compositions of n into sums of squares.

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 12*x^3 + 81*x^4 + 1335*x^5 + 49309*x^6 +...
where
log(A(x)) = x + 5*x^2/2 + 28*x^3/3 + 269*x^4/4 + 6181*x^5/5 + 286790*x^6/6 +...+ A219331(n^2)*x^n/n +...
		

Crossrefs

Cf. A224607, A219331, A006456, A224366.

Programs

PARI

{A219331(n)=n*polcoeff(-log(1-sum(r=1,sqrtint(n+1),x^(r^2)+x*O(x^n))),n)}
{a(n)=polcoeff(exp(sum(m=1,n,A219331(m^2)*x^m/m)+x*O(x^n)),n)}
for(n=0,20,print1(a(n),", "))

Formula

Logarithmic derivative yields A224607, where A224607(n) = A219331(n^2).