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A192204
G.f.: A(x) = exp( Sum_{n>=1} (Sum_{k=0..n} C(n,k)^4*A(x)^k) * x^n/n ).
0
1, 2, 13, 109, 1099, 12283, 147620, 1869346, 24633344, 334916467, 4669887745, 66481991644, 963096090267, 14160279233964, 210870471771803, 3175275874056722, 48281516978747396, 740504452581897112, 11444972742343813815
OFFSET
0,2
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 25 2011
STATUS
approved