OFFSET
0,5
COMMENTS
a(n) = n! - A057693(n). - Vaclav Kotesovec, Oct 09 2013
REFERENCES
R. Sedgewick and P. Flajolet, Analysis of Algorithms, Addison Wesley, 1996, page 358.
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: 1/(1-x) - exp(x + x^2/2 + x^3/3).
MAPLE
b:= proc(n) option remember; `if`(n<4, [6, 54, 444, 3828][n+1],
((5*n+3+n^2)*b(n-1) -(n+3)*b(n-2) -(n+3)*(n+2)*b(n-3)
-(n+3)*(n+2)*(n+1)^2*b(n-4))/n)
end:
a:= n-> `if`(n<4, 0, b(n-4)):
seq(a(n), n=0..30); # Alois P. Heinz, Jan 09 2013
MATHEMATICA
nn=25; Range[0, nn]!CoefficientList[Series[1/(1-x)-Exp[x+x^2/2+x^3/3], {x, 0, nn}], x]
(* Second program: *)
b[n_] := b[n] = If[n<4, {6, 54, 444, 3828}[[n+1]], ((5*n+3+n^2)*b[n-1] - (n + 3)*b[n-2] - (n+3)*(n+2)*b[n-3] - (n+3)*(n+2)*(n+1)^2*b[n-4])/n]; a[n_] := If[n<4, 0, b[n-4]]; Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 08 2017, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jan 09 2013
STATUS
approved