A092081 Triangle of certain double factorials.

1, 1, 2, 1, 3, 8, 1, 4, 15, 48, 1, 5, 24, 105, 384, 1, 6, 35, 192, 945, 3840, 1, 7, 48, 315, 1920, 10395, 46080, 1, 8, 63, 480, 3465, 23040, 135135, 645120, 1, 9, 80, 693, 5760, 45045, 322560, 2027025, 10321920, 1, 10, 99, 960, 9009, 80640, 675675, 5160960

Offset

0,3

Comments

This is the rectangular array A(3;m,n) := (2*n+m)!!/m!!, m >= 0, n >= 0, read by SW-NE diagonals. For n!! see A006882 (double factorials).

Links

Table of n, a(n) for n=0..52.

W. Lang, First 9 rows.

Formula

a(m, n)=(n+m)!!/(m-n)!!, 0<=n<=m, else 0, with 0!! := 1.

Crossrefs

Diagonals give: A000165 (double factorials of 2*n), A001147(n+1), A002866, A051577-83.

Columns give: A000012 (powers of 1), A000027 (naturals >=2), A005563, 3*A077415, for n=0..3.

Sequence in context: A298096 A053190 A135299 * A203997 A057740 A320875

Adjacent sequences: A092078 A092079 A092080 * A092082 A092083 A092084

Keyword

nonn,easy,tabl

Author

Wolfdieter Lang, Mar 19 2004

Status

approved