A182958 G.f.: A(x) = x/Series_Reversion(x*G(x)) where G(x) = Sum_{n>=0} n!^2*x^n.

1, 1, 3, 26, 435, 11454, 429982, 21731604, 1422610371, 117184594070, 11870433500970, 1451034234272556, 210686605349115246, 35851934993572153260, 7068013569547157285340, 1598270770810393333641640

Offset: 0

Author

Paul D. Hanna, Dec 31 2010

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x + 3*x^2 + 26*x^3 + 435*x^4 + 11454*x^5 +...
G.f. satisfies A(x) = G(x/A(x)) where A(x*G(x)) = G(x) begins:
G(x) = 1 + x + 2!^2*x^2 + 3!^2*x^3 + 4!^2*x^4 + 5!^2*x^5 +...
so that:
A(x) = 1 + x/A(x) + 2!^2*x^2/A(x)^2 + 3!^2*x^3/A(x)^3 + 4!^2*x^4/A(x)^4 +...
		

Programs

PARI

{a(n)=polcoeff(x/serreverse(sum(m=1,n+1,(m-1)!^2*x^m)+x^2*O(x^n)),n)}

Formula

G.f. satisfies: A(x) = G(x/A(x)) where A(x*G(x)) = G(x) = Sum_{n>=0} n!^2*x^n.

G.f. satisfies: [x^n] A(x)^(n+1)/(n+1) = n!^2.