|
%I #2 Mar 30 2012 18:37:22
%S 1,1,4,27,284,4110,77424,1818474,51692080,1738555344,67979689200,
%T 3047234077800,154810558674144,8829473686348848,560819284547110848,
%U 39398646866759606160,3043158904460954177280,257091879144869492997120
%N E.g.f. A(x) = G(x)/x where G(x) is the e.g.f. of A179493.
%F Let G(x) denote the e.g.f. of A179493, then G(x) satisfies:
%F . L(x) = G(x)/(x*G'(x)) * L(G(x)) where L(x) = x + x*G(x); see A179493 for more formulas.
%F Let R = the Riordan array (A(x), x*A(x)), then the e.g.f. of column k in the matrix log of R equals (k+1)*(x + x^2*A(x)).
%e E.g.f.: A(x) = 1 + x + 4*x^2/2! + 27*x^3/3! + 284*x^4/4! +...
%e x + x^2*A(x) = x + 2*x^2/2! + 6*x^3/3! + 48*x^4/4! + 540*x^5/5! +...
%o (PARI) {a(n)=local(A=[1,1]);for(i=2,n, A=concat(A,0);G=x*Ser(A);A[ #A]=polcoeff(1+subst(G,x,G)+O(x^#A)-(1+G)*deriv(G)*x^2/G^2,#A-1)/(#A-2));if(n<0,0,n!*A[n+1])}
%Y Cf. A179493, A179421.
%K nonn
%O 0,3
%A _Paul D. Hanna_, Jul 23 2010
|
