A193038 G.f. A(x) satisfies: x = Sum_{n>=1} x^n*A(-x)^sigma(n), where sigma(n) = sum of divisors of n (A000203).

1, 1, 2, 6, 23, 101, 475, 2321, 11629, 59364, 307648, 1614724, 8567810, 45890927, 247817187, 1347819147, 7376472346, 40594360200, 224500075274, 1247028876157, 6954322550810, 38921347036195, 218541728743211, 1230754878156173, 6950114772716368

Offset: 0

Author

Paul D. Hanna, Jul 14 2011

Keywords

• nonn

Comments

Compare the g.f. to a g.f. C(x) of the Catalan numbers: x = Sum_{n>=1} x^n*C(-x)^(2*n-1).

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 23*x^4 + 101*x^5 + 475*x^6 +...
The g.f. satisfies:
x = x*A(-x) + x^2*A(-x)^3 + x^3*A(-x)^4 + x^4*A(-x)^7 + x^5*A(-x)^6 + x^6*A(-x)^12 +...+ x^n*A(-x)^A000203(n) +...
where A000203 begins: [1,3,4,7,6,12,8,15,13,18,12,28,14,24,24,31,...].
		

Crossrefs

Cf. A193036, A193037, A193039, A193040, A000203.

Programs

PARI

{a(n)=local(A=[1]);for(i=1,n,A=concat(A,0);A[#A]=polcoeff(sum(m=1,#A,(-x)^m*Ser(A)^sigma(m)),#A));if(n<0,0,A[n+1])}