A075779 Triangle T(n,k) = f(n,k,n-1), n >= 2, 1 <= k <= n-1, where f is given below.

2, 6, 6, 12, 16, 12, 20, 35, 35, 20, 30, 66, 84, 66, 30, 42, 112, 175, 175, 112, 42, 56, 176, 328, 400, 328, 176, 56, 72, 261, 567, 819, 819, 567, 261, 72, 90, 370, 920, 1540, 1820, 1540, 920, 370, 90, 110, 506, 1419, 2706, 3696, 3696, 2706, 1419, 506, 110, 132, 672

Offset: 2

Author

N. J. A. Sloane, Oct 17 2002

Keywords

• nonn
• tabl

Comments

Row sums give sequence A033484(n)*(n+2). Essentially same triangle as A051597(n,k)*(n+2). - Philippe Deléham, Oct 01 2003

Examples

			2; 6,6; 12,16,12; 20,35,35,20; ...
		

Links

• Michel Lassalle, A new family of positive integers

Crossrefs

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).

Cf. A033484 A051597.

Programs

Maple

f := proc(n,p,k) convert( binomial(n,k)*hypergeom([1-k,-p,p-n],[1-n,1],1), `StandardFunctions`); end;

Mathematica

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 *)

Formula

f(n, p, k) = binomial(n, k)*hypergeom([1-k, -p, p-n], [1-n, 1], 1).