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

1, 4, 24, 196, 2040, 25924, 390264, 6804676, 135033720, 3007364164, 74315818104, 2018441506756, 59776933889400, 1917312391176004, 66216538949389944, 2449977966210378436, 96685769287005577080, 4053944607498740773444, 179973441341757042161784, 8433644996370680262923716

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Formula

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.

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

a(n) ~ (n-1)! * (1/log(3/2))^n. - Vaclav Kotesovec, May 23 2013

Example

E.g.f.: A(x) = x + 4*x^2/2! + 24*x^3/3! + 196*x^4/4! + 2040*x^5/5! +...
Note that A(x) = G(G(x)) where G(x) is an e.g.f. of A000629:
G(x) = x + 2*x^2/2! + 6*x^3/3! + 26*x^4/4! + 150*x^5/5! + 1082*x^6/6! +...

Mathematica

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

Prog

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

Crossrefs

Cf. A000629, A201731.

Sequence in context: A219530 A291819 A101370 * A362355 A099021 A220690

Adjacent sequences: A201335 A201336 A201337 * A201339 A201340 A201341

Keyword

nonn

Author

Paul D. Hanna, Dec 03 2011

Status

approved