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A198520 G.f. satisfies: A(x) = exp( Sum_{n>=1} A(x)^n / A(x^n) * x^n/n ). 1
1, 1, 1, 2, 4, 9, 22, 55, 141, 370, 986, 2662, 7264, 20006, 55534, 155219, 436456, 1233822, 3504482, 9996417, 28624038, 82248498, 237082689, 685375920, 1986604360, 5772399530, 16810591254, 49059068617, 143450142998, 420213814655, 1233034693847, 3623838769503 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..31.

EXAMPLE

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 4*x^4 + 9*x^5 + 22*x^6 + 55*x^7 +...

where

log(A(x)) = x +  A(x)^2/A(x^2)*x^2/2 + A(x)^3/A(x^3)*x^3/3 + A(x)^4/A(x^4)*x^4/4 +...

more explicitly,

log(A(x)) = x + x^2/2 + 4*x^3/3 + 9*x^4/4 + 26*x^5/5 + 76*x^6/6 + 218*x^7/7 +...

PROG

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

CROSSREFS

Cf. A198413.

Sequence in context: A274289 A265023 A290996 * A115324 A196307 A107092

Adjacent sequences:  A198517 A198518 A198519 * A198521 A198522 A198523

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 26 2011

STATUS

approved

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Last modified October 23 03:21 EDT 2019. Contains 328335 sequences. (Running on oeis4.)