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

%I #11 May 23 2013 09:42:09

%S 1,4,24,196,2040,25924,390264,6804676,135033720,3007364164,

%T 74315818104,2018441506756,59776933889400,1917312391176004,

%U 66216538949389944,2449977966210378436,96685769287005577080,4053944607498740773444,179973441341757042161784,8433644996370680262923716

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

%F 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 E.g.f.: log(1+x) o x/(1-2*x) o exp(x)-1, a composition of functions.

%F a(n) ~ (n-1)! * (1/log(3/2))^n. - _Vaclav Kotesovec_, May 23 2013

%e E.g.f.: A(x) = x + 4*x^2/2! + 24*x^3/3! + 196*x^4/4! + 2040*x^5/5! +...

%e Note that A(x) = G(G(x)) where G(x) is an e.g.f. of A000629:

%e G(x) = x + 2*x^2/2! + 6*x^3/3! + 26*x^4/4! + 150*x^5/5! + 1082*x^6/6! +...

%t Rest[CoefficientList[Series[Log[(2-E^x)/(3-2*E^x)], {x, 0, 20}], x]* Range[0, 20]!] (* _Vaclav Kotesovec_, May 23 2013 *)

%o (PARI) {a(n)=n!*polcoeff(log((2-exp(x+x*O(x^n)))/(3-2*exp(x+x*O(x^n)))),n)}

%Y Cf. A000629, A201731.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Dec 03 2011

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Last modified April 18 15:48 EDT 2024. Contains 371780 sequences. (Running on oeis4.)