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
Examples
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;
Programs
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PARI
T(n, k)=pollegendre(n-k, k)<<(n-k) \\ Charles R Greathouse IV, Mar 18 2017
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)}.
Comments