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%I #13 Jan 14 2014 10:01:18
%S 2,6,6,12,16,12,20,35,35,20,30,66,84,66,30,42,112,175,175,112,42,56,
%T 176,328,400,328,176,56,72,261,567,819,819,567,261,72,90,370,920,1540,
%U 1820,1540,920,370,90,110,506,1419,2706,3696,3696,2706,1419,506,110,132,672
%N Triangle T(n,k) = f(n,k,n-1), n >= 2, 1 <= k <= n-1, where f is given below.
%C Row sums give sequence A033484(n)*(n+2). Essentially same triangle as A051597(n,k)*(n+2). - _Philippe Deléham_, Oct 01 2003
%H Michel Lassalle, <a href="http://arXiv.org/abs/math.CO/0210208">A new family of positive integers</a>
%F f(n, p, k) = binomial(n, k)*hypergeom([1-k, -p, p-n], [1-n, 1], 1).
%e 2; 6,6; 12,16,12; 20,35,35,20; ...
%p f := proc(n,p,k) convert( binomial(n,k)*hypergeom([1-k,-p,p-n],[1-n,1],1), `StandardFunctions`); end;
%t t[n_, k_] := n*HypergeometricPFQ[{-k, 2-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 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).
%Y Cf. A033484 A051597.
%K nonn,tabl
%O 2,1
%A _N. J. A. Sloane_, Oct 17 2002
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