OFFSET
0,2
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..200
FORMULA
G.f.: sum(B(k)*k!*x^(k-2)*(1-x)^k, k>=2), where B(k) = sum(1/C(k,i), i=1..k-1).
a(n) ~ 2*n*n!/exp(1). - Vaclav Kotesovec, Jul 08 2013
MAPLE
a:= proc(n) option remember; `if`(n<6, [1, 2, 5, 20, 104, 632][n+1],
((3*n+10)*(n+3)*a(n-1) -(n+13)*(n+2)^2*a(n-2)
+(n+3)*(4*n^2+19*n+2)*a(n-3) -2*(n+2)*(3*n^2+6*n-4)*a(n-4)
+(4*n^3+8*n^2-12*n-4)*a(n-5) -n*(n+3)*(n-2)*a(n-6))/(2*n+4))
end:
seq(a(n), n=0..30); # Alois P. Heinz, Jul 01 2013
MATHEMATICA
f[n_] := Sum[Binomial[n-k+1, k] (-1)^k (n-k+1)!, {k, 0, Quotient[n+1, 2]}];
a[n_] := Sum[f[k] f[n-k], {k, 0, n}];
Table[a[n], {n, 0, 30}] (* Jean-François Alcover, Feb 14 2023 *)
PROG
(Maxima) f(n):=sum(binomial(n-k+1, k)*(-1)^k*(n-k+1)!, k, 0, floor((n+1)/2)); a(n):=sum(f(k)*f(n-k), k, 0, n); makelist(a(n), n, 0, 20);
CROSSREFS
KEYWORD
nonn
AUTHOR
Emanuele Munarini, Jul 01 2013
STATUS
approved