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A200215 G.f. satisfies: A(x) = exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^3 * x^k*A(x)^k] * x^n*A(x)^n/n ). 0
1, 1, 3, 13, 61, 306, 1623, 8937, 50565, 292283, 1718827, 10250916, 61854848, 376949934, 2316738789, 14343701657, 89379109846, 560108223900, 3527723269978, 22318890516413, 141778326349191, 903936594232782, 5782447430948438, 37102633354583532, 238729798670985104 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..24.

EXAMPLE

G.f.: A(x) = 1 + x + 3*x^2 + 13*x^3 + 61*x^4 + 306*x^5 + 1623*x^6 +...

where the logarithm of the g.f. A = A(x) equals the series:

log(A(x)) = (1 + x*A)*x*A + (1 + 2^3*x*A + x^2*A^2)*x^2*A^2/2 +

(1 + 3^3*x*A + 3^3*x^2*A^2 + x^3*A^3)*x^3*A^3/3 +

(1 + 4^3*x*A + 6^3*x^2*A^2 + 4^3*x^3*A^3 + x^4*A^4)*x^4*A^4/4 +

(1 + 5^3*x*A + 10^3*x^2*A^2 + 10^3*x^3*A^3 + 5^3*x^4*A^4 + x^5*A^5)*x^5*A^5/5 +

(1 + 6^3*x*A + 15^3*x^2*A^2 + 20^3*x^3*A^3 + 15^3*x^4*A^4 + 6^3*x^5*A^5 + x^6*A^6)*x^6*A^6/6 +...

more explicitly,

log(A(x)) = x + 5*x^2/2 + 31*x^3/3 + 185*x^4/4 + 1126*x^5/5 + 7043*x^6/6 + 44689*x^7/7 + 286241*x^8/8 +...

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*x^j*A^j)*(x*A+x*O(x^n))^m/m))); polcoeff(A, n, x)}

CROSSREFS

Cf. A198944, A200212, A192131, A166896, A199875, A166990, A198950, A181143, A181543.

Sequence in context: A026704 A046748 A256333 * A074548 A243014 A258799

Adjacent sequences:  A200212 A200213 A200214 * A200216 A200217 A200218

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 14 2011

STATUS

approved

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Last modified August 7 11:38 EDT 2022. Contains 355985 sequences. (Running on oeis4.)