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A297704 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.

%I A297704 #10 Jan 08 2018 03:34:19
%S A297704 1,3,1,15,6,1,93,39,9,1,645,276,72,12,1,4791,2073,576,114,15,1,37275,
%T A297704 16242,4689,1020,165,18,1,299865,131295,38889,8979,1635,225,21,1,
%U A297704 2474025,1087080,327960,78888,15510,2448,294,24,1
%N A297704 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 A297704 Peter Luschny, <a href="/A297704/b297704.txt">row n for n = 0..44</a>
%e A297704 Triangle starts:
%e A297704 [0]     1
%e A297704 [1]     3,     1
%e A297704 [2]    15,     6,    1
%e A297704 [3]    93,    39,    9,    1
%e A297704 [4]   645,   276,   72,   12,   1
%e A297704 [5]  4791,  2073,  576,  114,  15,  1
%e A297704 [6] 37275, 16242, 4689, 1020, 165, 18, 1
%t A297704 T[n_, k_] := Binomial[n, k] Hypergeometric2F1[k - n, n + 1, k + 2, -2];
%t A297704 Table[T[n, k], {n, 0, 6}, {k, 0, n}] // Flatten
%Y A297704 T(n, 0) = A103210(n).
%Y A297704 Row sums are A243626(n+1).
%K A297704 nonn,tabl
%O A297704 0,2
%A A297704 _Peter Luschny_, Jan 07 2018