A129547 a(n)= n! - (n-1)!! - a(n-1), with a(1)=1!-0!!=0.

0, 1, 3, 18, 94, 611, 4381, 35834, 326662, 3301193, 36611767, 442379438, 5784595282, 81393560783, 1226280162097, 19696507698878, 335990910075202, 6066382761193373, 115578717461844067, 2317323290060066858

Offset

0,3

Links

Table of n, a(n) for n=0..19.

Formula

a(n)= n! - (n-1)!! - a(n-1), with a(1)=1!-0!!=0. a(n)=abs{sum{i=1..n,[(n-i+1)!-(n-i)!! ]*(-1)^i}}

Example

a(1)=1!-0!!=1-1=0
a(2)=2!-1!!-1!+0!!=2-1-1+1=1
a(3)=3!-2!!-2!+1!!+1!-0!!=6-2-2+1+1-1=3
a(4)=4!-3!!-3!+2!!+2!-1!!-1!+0!!=24-3-6+2+2-1-1+1=18
a(5)=5!-4!!-4!+3!!+3!-2!!-2!+1!!+1!-0!!=120-8-24+3+6-2-2+1+1-1=94

Maple

P:=proc(n) local a, i, k, w; print(0); a:=0; for i from 2 by 1 to n do k:=i-1; w:=i-3; while w>0 do k:=k*w; w:=w-2; od; a:=(i!-k)-a; print(a); od; end: P(50);

Crossrefs

Sequence in context: A363647 A058409 A125833 * A081151 A132848 A321032

Adjacent sequences: A129544 A129545 A129546 * A129548 A129549 A129550

Keyword

nonn

Author

Paolo P. Lava and Giorgio Balzarotti, May 30 2007

Status

approved