OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: (4*(exp(-x)-1)+4*x-x^2)/(2*(1-x)^2).
a(n) = (2*n-1)*a(n-1) - (n-2)*(n-1)*a(n-2) - (n-2)*(n-1)*a(n-3). - Vaclav Kotesovec, Nov 19 2012
a(n) ~ n!*n*(4*exp(-1)-1)/2. - Vaclav Kotesovec, Nov 19 2012
a(n) = Sum_{k=1..floor(n/2)} k * A097592(n,k). - Alois P. Heinz, Jul 04 2019
EXAMPLE
Example: a(3)=4 because we have 123,(13)2,2(13),(23)1,3(12),321 (runs of even length shown between parentheses).
MAPLE
G:=(4*(exp(-x)-1)+4*x-x^2)/2/(1-x)^2: Gser:=series(G, x=0, 25): 0, seq(n!*coeff(Gser, x^n), n=1..24);
MATHEMATICA
Table[n!*SeriesCoefficient[(4*(E^(-x)-1)+4*x-x^2)/(2*(1-x)^2), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Nov 19 2012 *)
PROG
(PARI) x='x+O('x^66); concat([0, 0], Vec(serlaplace((4*(exp(-x)-1)+4*x-x^2)/(2*(1-x)^2)))) \\ Joerg Arndt, May 11 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
Emeric Deutsch, Aug 29 2004
STATUS
approved