OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
E.g.f.: (exp(x)*(20*x^3+30*x-30)+x+30)/(x-1)^2.
a(n) ~ n! * (20*exp(1)+31)*n. - Vaclav Kotesovec, Sep 12 2013
MAPLE
a:= proc(n) option remember; `if`(n<4, [0, 1, 34, 378][n+1],
((2*n^2-4*n+6)*a(n-1) -(n^3-3*n^2+13*n-10)*a(n-2)
+2*(2*n-1)*(n-2)*a(n-3) +(n-3)*(n-2)^2*a(n-4)) /(n-2))
end:
seq(a(n), n=0..30);
MATHEMATICA
a[n_] := With[{k = 5}, 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