A179494 E.g.f. A(x) = G(x)/x where G(x) is the e.g.f. of A179493.

1, 1, 4, 27, 284, 4110, 77424, 1818474, 51692080, 1738555344, 67979689200, 3047234077800, 154810558674144, 8829473686348848, 560819284547110848, 39398646866759606160, 3043158904460954177280, 257091879144869492997120

Offset: 0

Author

Paul D. Hanna, Jul 23 2010

Keywords

• nonn

Examples

			E.g.f.: A(x) = 1 + x + 4*x^2/2! + 27*x^3/3! + 284*x^4/4! +...
x + x^2*A(x) = x + 2*x^2/2! + 6*x^3/3! + 48*x^4/4! + 540*x^5/5! +...
		

Crossrefs

Cf. A179493, A179421.

Programs

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])}

Formula

Let G(x) denote the e.g.f. of A179493, then G(x) satisfies:

. L(x) = G(x)/(x*G'(x)) * L(G(x)) where L(x) = x + x*G(x); see A179493 for more formulas.

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)).