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URL: https://oeis.org/A198946

⇱ A198946 - OEIS

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A198946
G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^n * A(x)^k] * x^n/n ).
1
1, 2, 7, 43, 661, 45503, 14835966, 19030289368, 96523753164218, 1826134533496656481, 136782939777235335759015, 38134547664565961218637677016, 42464787999263932204904982967955033, 176203582974534986934299369142808689004350
OFFSET
0,2
EXAMPLE
G.f.: A(x) = 1 + 2*x + 7*x^2 + 43*x^3 + 661*x^4 + 45503*x^5 +...
where
log(A(x)) = (1 + A(x))*x + (1 + 2^2*A(x) + A(x)^2)*x^2/2 +
(1 + 3^3*A(x) + 3^3*A(x)^2 + A(x)^3)*x^3/3 +
(1 + 4^4*A(x) + 6^4*A(x)^2 + 4^4*A(x)^3 + A(x)^4)*x^4/4 +
(1 + 5^5*A(x) + 10^5*A(x)^2 + 10^5*A(x)^3 + 5^5*A(x)^4 + A(x)^5)*x^5/5 +...
more explicitly,
log(A(x)) = 2*x + 10*x^2/2 + 95*x^3/3 + 2298*x^4/4 + 220502*x^5/5 + 88457005*x^6/6 +...
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)^m*(A+x*O(x^n))^j)*x^m/m))); polcoeff(A, n, x)}
CROSSREFS
Cf. A198945.
Sequence in context: A228230 A340335 A011835 * A212270 A270348 A270580
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 31 2011
STATUS
approved