OFFSET
1,2
COMMENTS
The harmonic triangle uses the terms of this sequence as denominators, with numerators = 1: (1/1; 1/2, 1/2; 1/2, 1/6, 1/3; 1/2, 1/6, 1/12, 1/4; 1/2, 1/6, 1/12, 1/10, 1/5; ...). Row sums of the harmonic triangle = 1.
FORMULA
Denominators of the inverse of A127949; numerators = 1. Triangle read by rows, first (n-1) terms of 1*2, 2*3, 3*4, ...; followed by "n".
T(n,k) = k*(k+1) = A002378(k) for k < n; T(n,n) = n. - Andrés Ventas, Mar 26 2021
EXAMPLE
Triangle T(n,k) begins:
1;
2, 2;
2, 6, 3;
2, 6, 12, 4;
2, 6, 12, 20, 5;
2, 6, 12, 20, 30, 6;
2, 6, 12, 20, 30, 42, 7;
...
1/1 = 1,
1/2 + 1/2 = 1,
1/2 + 1/6 + 1/3 = 1,
1/2 + 1/6 + 1/12 + 1/4 = 1, etc.
MAPLE
A126615 := (n, k) -> `if`(n=k, n, 1/Beta(k, 2));
seq(print(seq(A126615(n, k), k=1..n)), n=1..9); # Peter Luschny, Jul 27 2014
MATHEMATICA
Flatten@Table[{Array[2PolygonalNumber@#&, n], n+1}, {n, 0, 10}] (* Giorgos Kalogeropoulos, Mar 31 2021 *)
CROSSREFS
KEYWORD
AUTHOR
Gary W. Adamson, Feb 09 2007
EXTENSIONS
Gary W. Adamson submitted two different triangles numbered A127899 based on the harmonic numbers. This is the second of them, which I am renumbering as A126615. Unfortunately there were several other entries defined in terms of "A127899" and I may not have guessed which version of A127899 was being referred to. - N. J. A. Sloane, Jan 09 2007
More terms from Philippe Deléham, Dec 17 2008
STATUS
approved