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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.
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%I #20 Jul 26 2023 11:44:35

%S 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 129,42,9,1,1024,1120,832,450,180,52,10,1,2304,2816,2352,1452,681,242,

%U 63,11,1,5120,6912,6400,4424,2364,985,316,75,12,1

%N 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 This triangle results when the first column is removed from A210038. - _Georg Fischer_, Jul 26 2023

%e Triangle starts:

%e 1;

%e 4, 1;

%e 12, 5, 1;

%e 32, 18, 6, 1;

%e 80, 56, 25, 7, 1;

%e 192, 160, 88, 33, 8, 1;

%e 448, 432, 280, 129, 42, 9, 1;

%e 1024, 1120, 832, 450, 180, 52, 10, 1;

%p T := (n,k) -> binomial(n+1,k+1)*hypergeom([k-n, k-n-1], [-n-1], -1):

%p seq(seq(simplify(T(n,k)),k=0..n),n=0..9);

%t T[n_, k_] := Binomial[n+1, k+1] HypergeometricPFQ[{k-n, k-n-1}, {-n-1}, -1];

%t Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jul 22 2019 *)

%Y A258109 (row sums), A008466 (alternating row sums), A001787 (col. 0), A001793 (col. 1), A055585 (col. 2).

%Y Cf. A210038.

%K nonn,tabl

%O 0,2

%A _Peter Luschny_, Apr 25 2016