cp's OEIS Frontend

A179423 E.g.f. A(x) = F(x)^2 where F(x) is the e.g.f. of A179421.

%I A179423 #2 Mar 30 2012 18:37:22
%S A179423 1,2,10,90,1240,23800,598788,18932620,729558240,33475442400,
%T A179423 1796086010400,111058345494624,7820581741096320,621007886404464000,
%U A179423 55143814204485434400,5436629250445000648800,591426542480093093242368
%N A179423 E.g.f. A(x) = F(x)^2 where F(x) is the e.g.f. of A179421.
%C A179423 Let F(x) be the e.g.f. of A179421, then x*F(x) equals the e.g.f. of column 0 in the matrix log of the Riordan array (F(x), x*F(x)).
%F A179423 a(n) = Sum_{k=0..n} C(n,k)*A179421(k)*A179421(n-k).
%e A179423 E.g.f.: A(x) = 1 + 2*x + 10*x^2/2! + 90*x^3/3! + 1240*x^4/4! +...
%e A179423 The e.g.f. of A179421 is:
%e A179423 F(x) = 1 + x + 4*x^2/2! + 33*x^3/3! + 440*x^4/4! + 8380*x^5/5! +...
%o A179423 (PARI) {a(n)=local(A=1+2*x+sum(m=2,n-1,a(m)*x^m/m!)+x*O(x^n),B=truncate(sqrt(A+O(x^n))));if(n<2,n!*polcoeff(A,n),n!*polcoeff((B+polcoeff(subst(x*B,x,x*B+x^2*O(x^n))/x,n)*x^n/(n-1)+x*O(x^n))^2,n))}
%Y A179423 Cf. A179421.
%K A179423 nonn
%O A179423 0,2
%A A179423 _Paul D. Hanna_, Jul 28 2010