A178087 G.f. satisfies: A(x) = Sum_{n>=0} x^n * Product_{k=1..n} A(k*x).

1, 1, 2, 6, 25, 141, 1071, 11011, 154739, 3005187, 81434048, 3101253384, 166823865867, 12719913809811, 1378095292930494, 212524751143894194, 46713381928627546015, 14648866052370410611923, 6558913185973371123604314, 4195585528812861561212654010

Offset: 0

Author

Paul D. Hanna, May 19 2010

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 2*x^2 + 6*x^3 + 25*x^4 + 141*x^5 +...
where
A(x) = 1 + x*A(x) + x^2*A(x)*A(2*x) + x^3*A(x)*A(2*x)*A(3*x) + x^4*A(x)*A(2*x)*A(3*x)*A(4*x) + x^5*A(x)*A(2*x)*A(3*x)*A(4*x)*A(5*x) +...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..60

Crossrefs

Cf. A230317.

Programs

PARI

{a(n)=local(A=1+x); for(i=1, n, A=1+sum(m=1, n, x^m*prod(k=1, m, subst(A, x, k*x+x*O(x^n))))); polcoeff(A, n)}
for(n=0,20,print1(a(n),", "))