A110124 A scaled Legendre triangle.

1, 0, 1, -2, 2, 1, 0, 4, 4, 1, 6, 8, 22, 6, 1, 0, 16, 136, 52, 8, 1, -20, 32, 886, 504, 94, 10, 1, 0, 64, 5944, 5136, 1232, 148, 12, 1, 70, 128, 40636, 53856, 16966, 2440, 214, 14, 1, 0, 256, 281488, 575296, 240368, 42256, 4248, 292, 16, 1, -252, 512, 1968934, 6225792, 3468844, 752800, 88566, 6776, 382, 18, 1

Offset

0,4

Comments

Row sums are A110125. Diagonal sums are A110126. Columns include A000079, A069835, A084773, and A098269.

Links

Table of n, a(n) for n=0..65.

Formula

Number triangle T(n, k)=2^(n-k)*LegendreP(n-k, k); T(n, k)=sum{j=0..floor((n-k)/2), (-1)^j*C(n-k, j)C(2n-2k-2j, n-k)k^(n-k-2j)}.

Example

Rows begin
1;
0,1;
-2,2,1;
0,4,4,1;
6,8,22,6,1;
0,16,136,62,8,1;
-20,32,886,504,94,10,1;

Prog

(PARI) T(n, k)=pollegendre(n-k, k)<<(n-k) \\ Charles R Greathouse IV, Mar 18 2017

Crossrefs

Sequence in context: A171941 A071464 A071510 * A116389 A216344 A332011

Adjacent sequences: A110121 A110122 A110123 * A110125 A110126 A110127

Keyword

easy,sign,tabl

Author

Paul Barry, Jul 13 2005

Status

approved