cp's OEIS Frontend

A201338 E.g.f.: log((2 - exp(x))/(3 - 2*exp(x))).

%I A201338 #11 May 23 2013 09:42:09
%S A201338 1,4,24,196,2040,25924,390264,6804676,135033720,3007364164,
%T A201338 74315818104,2018441506756,59776933889400,1917312391176004,
%U A201338 66216538949389944,2449977966210378436,96685769287005577080,4053944607498740773444,179973441341757042161784,8433644996370680262923716
%N A201338 E.g.f.: log((2 - exp(x))/(3 - 2*exp(x))).
%F A201338 E.g.f.: G(G(x)) where G(x) = log(1/(2-exp(x))) is an e.g.f. of A000629 (with offset 1), where A000629(n) is the number of necklaces of partitions of n+1 labeled beads.
%F A201338 E.g.f.: log(1+x) o x/(1-2*x) o exp(x)-1, a composition of functions.
%F A201338 a(n) ~ (n-1)! * (1/log(3/2))^n. - _Vaclav Kotesovec_, May 23 2013
%e A201338 E.g.f.: A(x) = x + 4*x^2/2! + 24*x^3/3! + 196*x^4/4! + 2040*x^5/5! +...
%e A201338 Note that A(x) = G(G(x)) where G(x) is an e.g.f. of A000629:
%e A201338 G(x) = x + 2*x^2/2! + 6*x^3/3! + 26*x^4/4! + 150*x^5/5! + 1082*x^6/6! +...
%t A201338 Rest[CoefficientList[Series[Log[(2-E^x)/(3-2*E^x)], {x, 0, 20}], x]* Range[0, 20]!] (* _Vaclav Kotesovec_, May 23 2013 *)
%o A201338 (PARI) {a(n)=n!*polcoeff(log((2-exp(x+x*O(x^n)))/(3-2*exp(x+x*O(x^n)))),n)}
%Y A201338 Cf. A000629, A201731.
%K A201338 nonn
%O A201338 1,2
%A A201338 _Paul D. Hanna_, Dec 03 2011