cp's OEIS Frontend

A168450 G.f. A(x) satisfies: A(x) = G(x*A(x)) where A(x/G(x)) = G(x) = g.f. of A004304, where A004304(n) is the number of planar tree-rooted maps with n edges.

%I A168450 #4 Jun 14 2018 09:54:26
%S A168450 1,2,6,26,148,1012,7824,65886,590452,5546972,54070432,542937320,
%T A168450 5586265280,58659600352,626702981084,6795682231830,74645847739012,
%U A168450 829257675740724,9304974123394272,105343378754088424
%N A168450 G.f. A(x) satisfies: A(x) = G(x*A(x)) where A(x/G(x)) = G(x) = g.f. of A004304, where A004304(n) is the number of planar tree-rooted maps with n edges.
%H A168450 Vaclav Kotesovec, <a href="/A168450/b168450.txt">Table of n, a(n) for n = 0..850</a>
%F A168450 G.f.: A(x) = F(x/A(x)) where A(x*F(x)) = F(x) = g.f. of A005568, where A005568(n) is the product of two successive Catalan numbers C(n)*C(n+1).
%F A168450 G.f.: A(x) = x/Series_Reversion(x*F(x)) where F(x) = g.f. of A005568.
%F A168450 G.f.: A(x) = (1/x)*Series_Reversion(x/G(x)) where G(x) = g.f. of A004304.
%e A168450 G.f. A(x) = 1 + 2*x + 6*x^2 + 26*x^3 + 148*x^4 + 1012*x^5 + 7824*x^6 +...
%e A168450 A(x) satisfies: A(x*F(x)) = F(x) = g.f. of A005568:
%e A168450 F(x) = 1 + 2*x + 10*x^2 + 70*x^3 + 588*x^4 + 5544*x^5 + 56628*x^6 +...+ A000108(n)*A000108(n+1)*x^n +...
%e A168450 A(x) satisfies: A(x/G(x)) = G(x) = g.f. of A004304:
%e A168450 G(x) = 1 + 2*x + 2*x^2 + 6*x^3 + 28*x^4 + 160*x^5 + 1036*x^6 +...
%o A168450 (PARI) {a(n)=local(C_2=vector(n+1,m,(binomial(2*m-2,m-1)/m)*(binomial(2*m,m)/(m+1))));polcoeff((x/serreverse(x*Ser(C_2))),n)}
%Y A168450 Cf. A004304, A005568, A000108, variant: A168344.
%K A168450 nonn
%O A168450 0,2
%A A168450 _Paul D. Hanna_, Nov 26 2009