OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..444
FORMULA
E.g.f.: x/(1-x^2)*exp(x/(1-x)).
a(n) = n*a(n-1) + n^2*a(n-2) - (n-2)^2*n*a(n-3). - Vaclav Kotesovec, Sep 29 2013
a(n) ~ sqrt(2)/4 * n^(n+1/4)*exp(2*sqrt(n)-n-1/2) * (1 + 7/(48*sqrt(n))). - Vaclav Kotesovec, Sep 29 2013
MAPLE
G:=(x/(1-x^2))*exp(x/(1-x)): Gser:=series(G, x=0, 25): seq(n!*coeff(Gser, x^n), n=1..22); # Emeric Deutsch
# second Maple program:
b:= proc(n) option remember; `if`(n=0, [1, 0], add(
(p-> p+`if`(j::odd, [0, p[1]], 0))(b(n-j)*
binomial(n-1, j-1)*j!), j=1..n))
end:
a:= n-> b(n, 0)[2]:
seq(a(n), n=0..25); # Alois P. Heinz, May 10 2016
MATHEMATICA
Rest[CoefficientList[Series[x/(1-x^2)*E^(x/(1-x)), {x, 0, 20}], x]* Range[0, 20]!] (* Vaclav Kotesovec, Sep 29 2013 *)
nxt[{n_, a_, b_, c_}]:={n+1, b, c, (n+1)*c+(n+1)^2*b-(n-1)^2 (n+1)*a}; NestList[ nxt, {2, 0, 1, 2}, 30][[All, 2]] (* Harvey P. Dale, Jan 13 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Feb 19 2005
EXTENSIONS
More terms from Emeric Deutsch, Jun 24 2005
a(0)=0 pepended by Alois P. Heinz, May 10 2016
STATUS
approved