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

0, 3, 3, 12, 14, 12, 30, 45, 45, 30, 60, 114, 138, 114, 60, 105, 245, 357, 357, 245, 105, 168, 468, 808, 960, 808, 468, 168, 252, 819, 1647, 2286, 2286, 1647, 819, 252, 360, 1340, 3090, 4935, 5740, 4935, 3090, 1340, 360, 495, 2079, 5423, 9834, 13090, 13090, 9834, 5423

Offset

2,2

Links

Table of n, a(n) for n=2..54.

Michel Lassalle, A new family of positive integers

Formula

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

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*(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 *)

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).

Sequence in context: A117856 A074850 A073055 * A292515 A078666 A290438

Adjacent sequences: A075777 A075778 A075779 * A075781 A075782 A075783

Keyword

nonn,tabl

Author

N. J. A. Sloane, Oct 17 2002

Status

approved