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

0,3

Links

Table of n, a(n) for n=0..17.

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)).

Example

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! +...

Prog

(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])}

Crossrefs

Cf. A179493, A179421.

Sequence in context: A193467 A357174 A377811 * A295255 A203157 A304340

Adjacent sequences: A179491 A179492 A179493 * A179495 A179496 A179497

Keyword

nonn

Author

Paul D. Hanna, Jul 23 2010

Status

approved