A075798 Triangle T(n,k) = f(n,k,n-1), n >= 0, 0 <= k <= n, where f is given below.

1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 16, 12, 1, 1, 20, 35, 35, 20, 1, 1, 30, 66, 84, 66, 30, 1, 1, 42, 112, 175, 175, 112, 42, 1, 1, 56, 176, 328, 400, 328, 176, 56, 1, 1, 72, 261, 567, 819, 819, 567, 261, 72, 1, 1, 90, 370, 920, 1540, 1820, 1540, 920, 370, 90, 1, 1, 110, 506, 1419, 2706, 3696, 3696, 2706, 1419, 506, 110, 1, 1, 132, 672

Offset: 1

Author

N. J. A. Sloane, Oct 17 2002

Keywords

• nonn
• tabl

Examples

			1; 1,1; 1,2,1; 1,6,6,1; ...
		

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).

Programs

Maple

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

Mathematica

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-1]; Table[t[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 17 2014 *)

Formula

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