A123881 Expansion of e.g.f.: exp( 2*(exp(x)-1)/(2-exp(x)) ).

1, 2, 10, 70, 626, 6774, 85714, 1238710, 20096146, 361205046, 7118099922, 152499926198, 3527182848786, 87554148952118, 2320744552177234, 65401560669438902, 1952122937140314002, 61507654345360320310, 2039679556472462415570, 70998682644763584004790

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..415

Formula

a(n) ~ n^(n-1/4) * exp(2*sqrt(n)/sqrt(log(2)) - n + 1/(2*log(2)) - 3/2) / (sqrt(2)*log(2)^(n+1/4)). - Vaclav Kotesovec, Jun 03 2013

Maple

seq(coeff(series(exp( 2*(exp(x)-1)/(2-exp(x)) ), x, n+1)*factorial(n), x, n), n = 0..20); # G. C. Greubel, Aug 08 2019

Mathematica

CoefficientList[Series[E^(2*(E^x-1)/(2-E^x)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Jun 03 2013 *)
Table[Sum[BellY[n, k, PolyLog[-Range[n], 1/2]], {k, 0, n}], {n, 0, 20}] (* Vladimir Reshetnikov, Nov 09 2016 *)

Prog

(PARI) my(x='x+O('x^20)); Vec(serlaplace( exp( 2*(exp(x)-1)/(2-exp(x)) ) )) \\ G. C. Greubel, Aug 08 2019
(Magma) m:=20; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!( Exp( 2*(Exp(x)-1)/(2-Exp(x)) ) )); [Factorial(n-1)*b[n]: n in [1..m]]; // G. C. Greubel, Aug 08 2019
(Sage) m = 20; T = taylor(exp( 2*(exp(x)-1)/(2-exp(x)) ), x, 0, m); [factorial(n)*T.coefficient(x, n) for n in (0..m)] # G. C. Greubel, Aug 08 2019

Crossrefs

Sequence in context: A005568 A036075 A212914 * A289680 A089845 A293962

Adjacent sequences: A123878 A123879 A123880 * A123882 A123883 A123884

Keyword

nonn

Author

Karol A. Penson, Oct 16 2006

Extensions

Terms a(17) onward added by G. C. Greubel, Aug 08 2019

Status

approved