OFFSET
0,2
FORMULA
a(n) = sum(C(n,k)*A013999(k), k=0..n).
G.f.: sum(k!*x^(k-1)*(1-2*x)^k/(1-x)^(2*k), k>=1).
a(n) ~ n * n!. - Vaclav Kotesovec, Nov 02 2023
MAPLE
a:= proc(n) option remember; `if`(n<4, [1, 2, 5, 18][n+1],
(n+6)*a(n-1)-(5*n+7)*a(n-2)+(8*n-7)*a(n-3)-(4*n-12)*a(n-4))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Jul 01 2013
MATHEMATICA
a[n_] := a[n] = If[n < 4, {1, 2, 5, 18}[[n + 1]], (n + 6)*a[n - 1] - (5*n + 7)*a[n - 2] + (8*n - 7)*a[n - 3] - (4*n - 12)*a[n - 4]];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Jun 04 2018, from Maple *)
PROG
(Maxima) f(n):=sum(binomial(n-k+1, k)*(-1)^k*(n-k+1)!, k, 0, floor((n+1)/2)); a(n):=sum(binomial(n, k)*f(k), k, 0, n); makelist(a(n), n, 0, 20);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Jul 01 2013
STATUS
approved