A024419 a(n) = n! (1/C(n,0) + 1/C(n,1) + ... + 1/C(n,[ n/2 ])).

1, 1, 3, 8, 34, 156, 924, 6144, 48096, 420480, 4134240, 44720640, 530444160, 6824805120, 94787884800, 1412038656000, 22464536371200, 380017225728000, 6811416338227200, 128936055177216000, 2570286167543808000, 53818546503794688000, 1180914445357903872000

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

Half-convolution of factorials (A000142) with itself. For the definition of the half-convolution of a sequence with itself see a comment to A201204. - Vladimir Reshetnikov, Oct 05 2016

Examples

			a(3)=3!*(1/1 + 1/3)=6*4/3=8.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..449

Crossrefs

Cf. A000142, A003149, A201204.

Programs

Maple

a:=proc(n) options operator, arrow: factorial(n)*(sum(1/binomial(n, k), k= 0.. floor((1/2)*n))) end proc: seq(a(n), n=0..21); # Emeric Deutsch, Oct 11 2007

Mathematica

Table[Sum[k! (n - k)!, {k, 0, n/2}], {n, 0, 20}] (* Vladimir Reshetnikov, Oct 05 2016 *)

PARI

a(n) = sum(k=0, n\2, k!*(n-k)!); \\ Michel Marcus, Oct 05 2016

Formula

G.f.: (G(x)^2+H(x))/2 where G(x) = Sum_{k>=0} k!*x^k and H(x) = Sum_{k>=0} k!^2*x^(2*k). - Vladeta Jovovic, Sep 22 2007

a(n) = Sum_{k=0..floor(n/2)} k!*(n-k)!. - Vladimir Reshetnikov, Oct 05 2016

Extensions

More terms from Emeric Deutsch, Oct 11 2007