cp's OEIS Frontend

A320904 T(n, k) = binomial(2*n + 1 - k, k)*hypergeom([1, 1, -k], [1, 2*(n - k + 1)], -1), triangle read by rows, T(n, k) for n >= 0 and 0 <= k <= n.

%I A320904 #15 Oct 04 2023 04:49:05
%S A320904 1,1,3,1,5,7,1,7,16,15,1,9,29,42,31,1,11,46,93,99,63,1,13,67,176,256,
%T A320904 219,127,1,15,92,299,562,638,466,255,1,17,121,470,1093,1586,1486,968,
%U A320904 511,1,19,154,697,1941,3473,4096,3302,1981,1023
%N A320904 T(n, k) = binomial(2*n + 1 - k, k)*hypergeom([1, 1, -k], [1, 2*(n - k + 1)], -1), triangle read by rows, T(n, k) for n >= 0 and 0 <= k <= n.
%e A320904 Triangle starts:
%e A320904 [0] 1
%e A320904 [1] 1,  3
%e A320904 [2] 1,  5,   7
%e A320904 [3] 1,  7,  16,  15
%e A320904 [4] 1,  9,  29,  42,   31
%e A320904 [5] 1, 11,  46,  93,   99,   63
%e A320904 [6] 1, 13,  67, 176,  256,  219,  127
%e A320904 [7] 1, 15,  92, 299,  562,  638,  466, 255
%e A320904 [8] 1, 17, 121, 470, 1093, 1586, 1486, 968, 511
%p A320904 T := (n, k) -> binomial(2*n + 1 - k, k)*hypergeom([1, 1, -k], [1, 2*(n-k+1)], -1):
%p A320904 for n from 0 to 11 do seq(simplify(T(n, k)), k = 0..n) od;
%t A320904 s={};For[n=0,n<19,n++,For[k=0,k<n+1,k++,AppendTo[s,2^(2*n+1-k)-Sum[Binomial[2*n+1-k,i],{i,0,2*n+1-2*k-1}]]]];s (* _Detlef Meya_, Oct 03 2023 *)
%Y A320904 Row sums are A105693(n-1).
%Y A320904 Cf. A097750.
%K A320904 nonn,tabl
%O A320904 0,3
%A A320904 _Peter Luschny_, Oct 28 2018