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A126615 Denominators in a harmonic triangle. 7
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, 2, 6, 12, 20, 30, 42, 56, 8, 2, 6, 12, 20, 30, 42, 56, 72, 9, 2, 6, 12, 20, 30, 42, 56, 72, 90, 10, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 11, 2, 6, 12, 20, 30, 42, 56, 72, 90, 110, 132, 12, 2, 6 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums = A006527: (1, 4, 11, 24, 45, 76,...). 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.

LINKS

Table of n, a(n) for n=1..80.

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".

EXAMPLE

First few rows of the triangle are:

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;

...

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

CROSSREFS

Cf. A000012, A051340, A127949, A006527, A003506.

Sequence in context: A078020 A097521 A081668 * A158524 A054274 A053695

Adjacent sequences:  A126612 A126613 A126614 * A126616 A126617 A126618

KEYWORD

nonn,tabl,frac

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

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Last modified October 18 14:11 EDT 2019. Contains 328161 sequences. (Running on oeis4.)