A182958 - OEIS

%I #9 Mar 30 2012 18:37:23

%S 1,1,3,26,435,11454,429982,21731604,1422610371,117184594070,

%T 11870433500970,1451034234272556,210686605349115246,

%U 35851934993572153260,7068013569547157285340,1598270770810393333641640

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

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

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

%e G.f.: A(x) = 1 + x + 3*x^2 + 26*x^3 + 435*x^4 + 11454*x^5 +...

%e G.f. satisfies A(x) = G(x/A(x)) where A(x*G(x)) = G(x) begins:

%e G(x) = 1 + x + 2!^2*x^2 + 3!^2*x^3 + 4!^2*x^4 + 5!^2*x^5 +...

%e so that:

%e 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 +...

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

%K nonn

%O 0,3

%A _Paul D. Hanna_, Dec 31 2010