A144895 Second column of triangle A134134 (S2'(2) = S1hat(2)).

1, 2, 10, 36, 204, 1104, 7776, 57600, 505440, 4803840, 51442560, 597784320, 7609593600, 104364288000, 1541746483200, 24329797632000, 409042632499200, 7290954768384000, 137384159367168000, 2727604332085248000, 56913717580296192000, 1244955414746824704000

Offset: 0

Author

Wolfdieter Lang, Oct 09 2008

Keywords

• nonn
• easy

Comments

Sum of the products of the factorials of the partition parts of n+2 into two parts. - Wesley Ivan Hurt, Mar 18 2016

Examples

			a(2)=10; The partitions of (2)+2 = 4 into two parts are: (3,1) and (2,2). The sum of the products of the factorials of the partition parts is: 3!*1! + 2!*2! = 6 + 4 = 10. - _Wesley Ivan Hurt_, Mar 18 2016
		

Crossrefs

Cf. A000142 (factorials, first column). A144896 (third column).

Cf. A134134.

Programs

Maple

A144895:=n->add(i!*(n-i+2)!, i=1..floor(n/2)+1): seq(A144895(n), n=0..30); # Wesley Ivan Hurt, Mar 18 2016

Mathematica

Table[Sum[i!*(n - i + 2)!, {i, Floor[n/2] + 1}], {n, 0, 20}] (* Wesley Ivan Hurt, Mar 18 2016 *)

Formula

a(n) = A134134(n+2,2), n>=0.

a(n) = Sum_{i=1..floor(n/2)+1} i! * (n-i+2)!. - Wesley Ivan Hurt, Mar 18 2016