OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: (exp(x)*(12*x^2-12*x+14)-x-14)/(x-1)^2.
a(n) ~ n! * (14*exp(1)-15)*n. - Vaclav Kotesovec, Sep 12 2013
MAPLE
a:= proc(n) option remember; `if`(n<3, [0, 1, 18][n+1],
((12*n^3-42*n^2+38*n+7)*a(n-1)-(n-1)*(6*n^3-12*n^2+n+14)*a(n-2)
+(n-1)*(n-2)*(6*n^2-12*n+7)*a(n-3))/(6*n^2-24*n+25))
end:
seq(a(n), n=0..30);
MATHEMATICA
a[n_] := With[{k = 4}, Sum[If[n==t, 1, (n!/(t+1)!)(t(n-t+1)+1-((t+1)(n-t)+1)/(t+2))] t^k, {t, 1, n}]];
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 10 2013
STATUS
approved