A145316 L-matrix for Hankel matrix of aerated factorials.

1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 2, 0, 4, 0, 1, 0, 6, 0, 6, 0, 1, 6, 0, 18, 0, 9, 0, 1, 0, 24, 0, 36, 0, 12, 0, 1, 24, 0, 96, 0, 72, 0, 16, 0, 1, 0, 120, 0, 240, 0, 120, 0, 20, 0, 1, 120, 0, 600, 0, 600, 0, 200, 0

Offset

0,8

Comments

Row sums are A056953. Hankel matrix of aerated factorials H=LDU where U=transpose of L. Aerated version of A104557.

Links

Table of n, a(n) for n=0..62.

Formula

Triangle T(n,k)=[k<=n]((n-k)/2)!C((n+k)/2-floor(k/2),floor((k+1)/2))C((n+k)/2-floor((k+1)/2),floor(k/2))(1+(-1)^(n-k))/2;

Example

Triangle begins 1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 2, 0, 4, 0, 1, 0, 6, 0, 6, 0, 1, 6, 0, 18, 0, 9, 0, 1, 0, 24, 0, 36, 0, 12, 0, 1, 24, 0, 96, 0, 72, 0, 16, 0, 1

Crossrefs

Sequence in context: A071491 A156537 A239501 * A137298 A136487 A178108

Adjacent sequences: A145313 A145314 A145315 * A145317 A145318 A145319

Keyword

easy,nonn,tabl

Author

Paul Barry, Oct 07 2008

Status

approved