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A272099 Triangle read by rows, T(n,k) = C(n+1,k+1)*F([k-n, k-n-1], [-n-1], -1), where F is the generalized hypergeometric function, for n>=0 and 0<=k<=n.

%I A272099 #20 Jul 26 2023 11:44:35
%S A272099 1,4,1,12,5,1,32,18,6,1,80,56,25,7,1,192,160,88,33,8,1,448,432,280,
%T A272099 129,42,9,1,1024,1120,832,450,180,52,10,1,2304,2816,2352,1452,681,242,
%U A272099 63,11,1,5120,6912,6400,4424,2364,985,316,75,12,1
%N A272099 Triangle read by rows, T(n,k) = C(n+1,k+1)*F([k-n, k-n-1], [-n-1], -1), where F is the generalized hypergeometric function, for n>=0 and 0<=k<=n.
%C A272099 This triangle results when the first column is removed from A210038. - _Georg Fischer_, Jul 26 2023
%e A272099 Triangle starts:
%e A272099 1;
%e A272099 4,    1;
%e A272099 12,   5,    1;
%e A272099 32,   18,   6,   1;
%e A272099 80,   56,   25,  7,   1;
%e A272099 192,  160,  88,  33,  8,   1;
%e A272099 448,  432,  280, 129, 42,  9,  1;
%e A272099 1024, 1120, 832, 450, 180, 52, 10, 1;
%p A272099 T := (n,k) -> binomial(n+1,k+1)*hypergeom([k-n, k-n-1], [-n-1], -1):
%p A272099 seq(seq(simplify(T(n,k)),k=0..n),n=0..9);
%t A272099 T[n_, k_] := Binomial[n+1, k+1] HypergeometricPFQ[{k-n, k-n-1}, {-n-1}, -1];
%t A272099 Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jul 22 2019 *)
%Y A272099 A258109 (row sums), A008466 (alternating row sums), A001787 (col. 0), A001793 (col. 1), A055585 (col. 2).
%Y A272099 Cf. A210038.
%K A272099 nonn,tabl
%O A272099 0,2
%A A272099 _Peter Luschny_, Apr 25 2016