cp's OEIS Frontend

A110124 A scaled Legendre triangle.

%I A110124 #6 Mar 18 2017 23:29:28
%S A110124 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,
%T A110124 1,0,64,5944,5136,1232,148,12,1,70,128,40636,53856,16966,2440,214,14,
%U A110124 1,0,256,281488,575296,240368,42256,4248,292,16,1,-252,512,1968934,6225792,3468844,752800,88566,6776,382,18,1
%N A110124 A scaled Legendre triangle.
%C A110124 Row sums are A110125. Diagonal sums are A110126. Columns include A000079, A069835, A084773, and A098269.
%F A110124 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)}.
%e A110124 Rows begin
%e A110124 1;
%e A110124 0,1;
%e A110124 -2,2,1;
%e A110124 0,4,4,1;
%e A110124 6,8,22,6,1;
%e A110124 0,16,136,62,8,1;
%e A110124 -20,32,886,504,94,10,1;
%o A110124 (PARI) T(n, k)=pollegendre(n-k, k)<<(n-k) \\ _Charles R Greathouse IV_, Mar 18 2017
%K A110124 easy,sign,tabl
%O A110124 0,4
%A A110124 _Paul Barry_, Jul 13 2005