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A075780 Triangle T(n,k) = f(n,k,n-2), n >= 2, 1 <= k <= n-1, where f is given below.

%I A075780 #9 Jan 14 2014 10:01:15
%S A075780 0,3,3,12,14,12,30,45,45,30,60,114,138,114,60,105,245,357,357,245,105,
%T A075780 168,468,808,960,808,468,168,252,819,1647,2286,2286,1647,819,252,360,
%U A075780 1340,3090,4935,5740,4935,3090,1340,360,495,2079,5423,9834,13090,13090,9834,5423
%N A075780 Triangle T(n,k) = f(n,k,n-2), n >= 2, 1 <= k <= n-1, where f is given below.
%H A075780 Michel Lassalle, <a href="http://arXiv.org/abs/math.CO/0210208">A new family of positive integers</a>
%F A075780 f(n, p, k) = binomial(n, k)*hypergeom([1-k, -p, p-n], [1-n, 1], 1).
%p A075780 f := proc(n,p,k) convert( binomial(n,k)*hypergeom([1-k,-p,p-n],[1-n,1],1), `StandardFunctions`); end;
%t A075780 t[n_, k_] := n*(n-1)/2*HypergeometricPFQ[{-k, 3-n, k-n}, {1, 1-n}, 1]; Table[t[n, k], {n, 2, 12}, {k, 1, n-1}] // Flatten (* _Jean-François Alcover_, Jan 14 2014 *)
%Y A075780 Cf. A014410 and A007318 for f(n, k, n), A075779 and A075798 for f(n, k, n-1) and A075780 and A075837 for f(n, k, n-2).
%K A075780 nonn,tabl
%O A075780 2,2
%A A075780 _N. J. A. Sloane_, Oct 17 2002