A075837 Triangle T(n,k) = f(n,k,n-2), n >= 0, 0 <= k <= n, where f is given below.
1, 1, 1, 1, 0, 1, 1, 3, 3, 1, 1, 12, 14, 12, 1, 1, 30, 45, 45, 30, 1, 1, 60, 114, 138, 114, 60, 1, 1, 105, 245, 357, 357, 245, 105, 1, 1, 168, 468, 808, 960, 808, 468, 168, 1, 1, 252, 819, 1647, 2286, 2286, 1647, 819, 252, 1, 1, 360, 1340, 3090, 4935, 5740, 4935, 3090, 1340, 360, 1, 1, 495, 2079, 5423, 9834, 13090, 13090, 9834, 5423
Offset: 1
Examples
1; 1,1; 1,0,1; 1,3,3,1; ...
Links
- Michel Lassalle, A new family of positive integers
Crossrefs
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-2]; Table[t[n, k], {n, 0, 11}, {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).