A108083 Triangle, read by rows, where T(0,0) = 1, T(n,k) = (-1)^n*(2n+1)*T(n-1,k) - T(n-1,k-1).

1, -3, -1, -15, -2, 1, 105, 29, -5, -1, 945, 156, -74, -4, 1, -10395, -2661, 658, 118, -7, -1, -135135, -24198, 11215, 876, -209, -6, 1, 2027025, 498105, -144027, -24355, 2259, 299, -9, -1, 34459425, 6440760, -2946564, -270008, 62758, 2824, -452, -8, 1, -654729075, -156833865, 49543956, 8076716

Offset

0,2

Comments

Row sums are (-1)^round(n/2) * 2^(2*n) * floor(n/2)! * round(n/2 + 1/2)!.

Links

Table of n, a(n) for n=0..48.

Example

Triangle begins
1;
-3, -1;
-15, -2, 1;
105, 29, -5, -1;
945, 156, -74, -4, 1;

Prog

(PARI) t(n, k) = {if (k < 0, return (0)); if (n < k, return (0)); if (n == 0, return (1)); return ((-1)^n*(2*n+1)*t(n-1, k) - t(n-1, k-1)); } \\ Michel Marcus, Apr 11 2013

Crossrefs

Sequence in context: A080924 A232179 A128042 * A163239 A134145 A134146

Adjacent sequences: A108080 A108081 A108082 * A108084 A108085 A108086

Keyword

sign,tabl

Author

Gerald McGarvey, Jun 04 2005

Status

approved