A192204 G.f.: A(x) = exp( Sum_{n>=1} (Sum_{k=0..n} C(n,k)^4*A(x)^k) * x^n/n ).

1, 2, 13, 109, 1099, 12283, 147620, 1869346, 24633344, 334916467, 4669887745, 66481991644, 963096090267, 14160279233964, 210870471771803, 3175275874056722, 48281516978747396, 740504452581897112, 11444972742343813815

Offset

0,2

Links

Table of n, a(n) for n=0..18.

Example

G.f.: A(x) = 1 + 2*x + 13*x^2 + 109*x^3 + 1099*x^4 + 12283*x^5 +...
which satisfies:
log(A(x)) = (1 + A(x))*x + (1 + 16*A(x) + A(x)^2)*x^2/2 + (1 + 81*A(x) + 81*A(x)^2 + A(x)^3)*x^3/3 + (1 + 256*A(x) + 1296*A(x)^2 + 256*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)^4*(A+x*O(x^n))^j)*x^m/m))); polcoeff(A, n, x)}

Crossrefs

Cf. variants: A007863, A192131.

Sequence in context: A264621 A367648 A245806 * A176932 A258916 A052444

Adjacent sequences: A192201 A192202 A192203 * A192205 A192206 A192207

Keyword

nonn

Author

Paul D. Hanna, Jun 25 2011

Status

approved