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

1, 2, 10, 90, 1240, 23800, 598788, 18932620, 729558240, 33475442400, 1796086010400, 111058345494624, 7820581741096320, 621007886404464000, 55143814204485434400, 5436629250445000648800, 591426542480093093242368

Offset: 0

Author

Paul D. Hanna, Jul 28 2010

Keywords

• nonn

Comments

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)).

Examples

			E.g.f.: A(x) = 1 + 2*x + 10*x^2/2! + 90*x^3/3! + 1240*x^4/4! +...
The e.g.f. of A179421 is:
F(x) = 1 + x + 4*x^2/2! + 33*x^3/3! + 440*x^4/4! + 8380*x^5/5! +...
		

Crossrefs

Cf. A179421.

Programs

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))}

Formula

a(n) = Sum_{k=0..n} C(n,k)*A179421(k)*A179421(n-k).