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

1,5

Links

Table of n, a(n) for n=1..81.

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).

Example

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

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 *)

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: A143185 A347675 A157635 * A155864 A145903 A223257

Adjacent sequences: A075795 A075796 A075797 * A075799 A075800 A075801

Keyword

nonn,tabl

Author

N. J. A. Sloane, Oct 17 2002

Status

approved