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A192131 G.f. satisfies: A(x) = exp( Sum_{n>=1} (Sum_{k=0..n} C(n,k)^3*A(x)^k) * x^n/n ). 4
1, 2, 9, 53, 357, 2611, 20180, 162276, 1344455, 11400944, 98498545, 864068233, 7677040177, 68947431898, 624960856374, 5710352911097, 52542826413590, 486458467209032, 4528570067254485, 42365044032385154, 398081015128641213 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

EXAMPLE

G.f.: A(x) = 1 + 2*x + 9*x^2 + 53*x^3 + 357*x^4 + 2611*x^5 + 20180*x^6 +...

where the g.f. satisfies:

log(A(x)) = (1 + A(x))*x + (1 + 8*A(x) + A(x)^2)*x^2/2 + (1 + 27*A(x) + 27*A(x)^2 + A(x)^3)*x^3/3 + (1 + 64*A(x) + 216*A(x)^2 + 64*A(x)^3 + A(x)^4)*x^4/4 +...

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(j=0, m, binomial(m, j)^3*(A+x*O(x^n))^j)*x^m/m))); polcoeff(A, n, x)}

CROSSREFS

Cf. A007863 (variant).

Sequence in context: A266469 A080146 A074602 * A326287 A231493 A218945

Adjacent sequences:  A192128 A192129 A192130 * A192132 A192133 A192134

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jun 24 2011

STATUS

approved

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Last modified June 19 00:04 EDT 2021. Contains 345125 sequences. (Running on oeis4.)