A179156 G.f. satisfies: A(x) = B(x*A(x)) where B(x) = Sum_{n>=0} x^n/n!^2 and A(x) = Sum_{n>=0} a(n)*x^n/n!^2.
1, 1, 5, 64, 1577, 64026, 3887167, 330394800, 37487397201, 5477556616750, 1002201757761971, 224502014115239136, 60447250689539460925, 19264011725572422723292, 7172619686789755991626485
Offset: 0
Keywords
Examples
G.f.: A(x) = 1 + x + 5*x^2/2!^2 + 64*x^3/3!^2 + 1577*x^4/4!^2 +...
where A(x) = Sum_{n>=0} x^n*A(x)^n/n!^2.
Also, A(x/B(x)) = B(x) = 1 + x + x^2/2!^2 + x^3/3!^2 + x^4/4!^2 +...
Crossrefs
Cf. A217567.
Programs
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PARI
{a(n)=local(B=sum(m=0,n,x^m/m!^2+O(x^(n+2))));n!^2*polcoeff(serreverse(x/B)/x,n)}
Formula
G.f.: A(x) = (1/x)*Series_Reversion(x/B(x)) where A(x/B(x)) = B(x) = Sum_{n>=0} x^n/n!^2.
a(n) = [x^n/n!^2] B(x)^(n+1)/(n+1).