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A075837 Triangle T(n,k) = f(n,k,n-2), n >= 0, 0 <= k <= n, where f is given below.

%I A075837 #10 Jan 17 2014 05:38:34
%S A075837 1,1,1,1,0,1,1,3,3,1,1,12,14,12,1,1,30,45,45,30,1,1,60,114,138,114,60,
%T A075837 1,1,105,245,357,357,245,105,1,1,168,468,808,960,808,468,168,1,1,252,
%U A075837 819,1647,2286,2286,1647,819,252,1,1,360,1340,3090,4935,5740,4935,3090,1340,360,1,1,495,2079,5423,9834,13090,13090,9834,5423
%N A075837 Triangle T(n,k) = f(n,k,n-2), n >= 0, 0 <= k <= n, where f is given below.
%H A075837 Michel Lassalle, <a href="http://arXiv.org/abs/math.CO/0210208">A new family of positive integers</a>
%F A075837 f(n, p, k) = binomial(n, k)*hypergeom([1-k, -p, p-n], [1-n, 1], 1).
%e A075837 1; 1,1; 1,0,1; 1,3,3,1; ...
%p A075837 f := proc(n,p,k) convert( binomial(n,k)*hypergeom([1-k,-p,p-n],[1-n,1],1), `StandardFunctions`); end;
%t A075837 f[n_, p_, k_] := Binomial[n, k]*HypergeometricPFQ[{1 - k, -p, p-n}, {1-n, 1}, 1]; t[n_, n_] = t[_, 0] = 1; t[n_, k_] := f[n, k, n-2]; Table[t[n, k], {n, 0, 11}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jan 17 2014 *)
%Y A075837 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 A075837 nonn,tabl
%O A075837 1,8
%A A075837 _N. J. A. Sloane_, Oct 17 2002