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A179494 E.g.f. A(x) = G(x)/x where G(x) is the e.g.f. of A179493. 1
1, 1, 4, 27, 284, 4110, 77424, 1818474, 51692080, 1738555344, 67979689200, 3047234077800, 154810558674144, 8829473686348848, 560819284547110848, 39398646866759606160, 3043158904460954177280, 257091879144869492997120 (list; graph; refs; listen; history; text; internal format)
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: A020558 A259485 A193467 * A295255 A203157 A119820

Adjacent sequences:  A179491 A179492 A179493 * A179495 A179496 A179497

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jul 23 2010

STATUS

approved

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Last modified December 13 00:17 EST 2017. Contains 295954 sequences.