A297704 - OEIS

%I #10 Jan 08 2018 03:34:19

%S 1,3,1,15,6,1,93,39,9,1,645,276,72,12,1,4791,2073,576,114,15,1,37275,

%T 16242,4689,1020,165,18,1,299865,131295,38889,8979,1635,225,21,1,

%U 2474025,1087080,327960,78888,15510,2448,294,24,1

%N Triangle read by rows, T(n,k) = binomial(n, k)*hypergeom2F1(k - n, n + 1, k + 2, -2) for n >= 0 and 0 <= k <= n.

%H Peter Luschny, <a href="/A297704/b297704.txt">row n for n = 0..44</a>

%e Triangle starts:

%e [0]     1

%e [1]     3,     1

%e [2]    15,     6,    1

%e [3]    93,    39,    9,    1

%e [4]   645,   276,   72,   12,   1

%e [5]  4791,  2073,  576,  114,  15,  1

%e [6] 37275, 16242, 4689, 1020, 165, 18, 1

%t T[n_, k_] := Binomial[n, k] Hypergeometric2F1[k - n, n + 1, k + 2, -2];

%t Table[T[n, k], {n, 0, 6}, {k, 0, n}] // Flatten

%Y T(n, 0) = A103210(n).

%Y Row sums are A243626(n+1).

%K nonn,tabl

%O 0,2

%A _Peter Luschny_, Jan 07 2018