A192131 G.f. satisfies: A(x) = exp( Sum_{n>=1} (Sum_{k=0..n} C(n,k)^3*A(x)^k) * x^n/n ).

1, 2, 9, 53, 357, 2611, 20180, 162276, 1344455, 11400944, 98498545, 864068233, 7677040177, 68947431898, 624960856374, 5710352911097, 52542826413590, 486458467209032, 4528570067254485, 42365044032385154, 398081015128641213

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: A367390 A080146 A074602 * A326287 A351815 A231493

Adjacent sequences: A192128 A192129 A192130 * A192132 A192133 A192134

Keyword

nonn

Author

Paul D. Hanna, Jun 24 2011

Status

approved