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A198413 G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x)^n * A(x^n) * x^n/n ). 1
1, 1, 3, 11, 46, 205, 962, 4668, 23268, 118374, 612305, 3210348, 17023682, 91140496, 491968036, 2674572509, 14631157562, 80480706331, 444865534251, 2469826058736, 13766223517639, 77003660186990, 432131032213098, 2432230966070833, 13726899289265314 (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 + 11*x^3 + 46*x^4 + 205*x^5 + 962*x^6 +...

where

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

more explicitly,

log(A(x)) = x + 5*x^2/2 + 25*x^3/3 + 133*x^4/4 + 716*x^5/5 + 3947*x^6/6 +...

PROG

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, subst(A, x, x^m+x*O(x^n))*(x*A+x*O(x^n))^m/m))); polcoeff(A, n)}

CROSSREFS

Cf. A198520.

Sequence in context: A151138 A151139 A301412 * A151140 A271959 A151141

Adjacent sequences:  A198410 A198411 A198412 * A198414 A198415 A198416

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 26 2011

STATUS

approved

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Last modified September 21 17:46 EDT 2019. Contains 327273 sequences. (Running on oeis4.)