A217989 G.f. satisfies: A(x) = 1+x + x^2*A'(x)*A(x)^2.

1, 1, 1, 4, 19, 116, 835, 6890, 63826, 654552, 7354893, 89830770, 1184915556, 16788863356, 254342837905, 4103256660048, 70241858430220, 1271839899568064, 24287699718766932, 487891841580468294, 10285169201486942788, 227042177973572054900

Offset: 0

Author

Paul D. Hanna, Oct 23 2012

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + x^2 + 4*x^3 + 19*x^4 + 116*x^5 + 835*x^6 + 6890*x^7 +...
Related expansions:
A'(x) = 1 + 2*x + 12*x^2 + 76*x^3 + 580*x^4 + 5010*x^5 + 48230*x^6 +...
A(x)^2 = 1 + 2*x + 3*x^2 + 10*x^3 + 47*x^4 + 278*x^5 + 1956*x^6 + 15834*x^7 +...
		

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..445

Crossrefs

Cf. A143916, A218223.

Programs

PARI

{a(n)=local(A=1+x); for(i=1, n, A=1+x+x^2*A'*(A^2+x*O(x^n))); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Formula

a(n) ~ c * n! * n, where c = 0.21362630601338471861707529847387... - Vaclav Kotesovec, Feb 22 2014