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Search: id:A126615
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| A126615 |
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Denominators in a harmonic triangle. |
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+0
7
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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.
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FORMULA
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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".
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EXAMPLE
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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;
...
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CROSSREFS
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Cf. A000012, A051340, A127949, A006527, A003506.
Sequence in context: A078020 A097521 A081668 this_sequence A158524 A054274 A053695
Adjacent sequences: A126612 A126613 A126614 this_sequence A126616 A126617 A126618
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KEYWORD
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nonn,tabl,frac
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 09 2007
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EXTENSIONS
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Gary 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 (njas(AT)research.att.com), Jan 09 2007
More terms from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Dec 17 2008
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