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Search: id:A118392
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| A118392 |
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Denominator of sum of reciprocals of first n tetrahedral numbers A000292. |
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+0
5
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| 1, 4, 20, 5, 7, 56, 24, 15, 55, 44, 52, 91, 35, 80, 272, 51, 57, 380, 140, 77, 253, 184, 200, 325, 117, 252, 812, 145, 155, 992
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Numerators are A118391. Fractions are: 1/1, 5/4, 27/20, 7/5, 10/7, 81/56, 35/24, 22/15, 81/55, 65/44, 77/52, 135/91, 52/35, 119/80, 405/272, 76/51, 85/57, 567/380, 209/140, 115/77, 378/253, 275/184, 299/200, 486/325, 175/117, 377/252, 1215/812, 217/145, 232/155, 1485/992. The denominator of sum of reciprocals of first n triangular numbers is A026741.
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FORMULA
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A118391(n)/A118392(n) = SUM[i=1..n] (1/A000292(n)). A118391(n)/A118392(n) = SUM[i=1..n] (1/C(n+2,3)). A118391(n)/A118392(n) = SUM[i=1..n] (1/(n*(n+1)*(n+2)/6)).
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EXAMPLE
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a(1) = 1 = denominator of 1/1.
a(2) = 4 = denominator of 5/4 = 1/1 + 1/4.
a(3) = 20 = denominator of 27/20 = 1/1 + 1/4 + 1/10.
a(4) = 5 = denominator of 7/5 = 1/1 + 1/4 + 1/10 + 1/20.
a(5) = 7 = denominator of 10/7 = 1/1 + 1/4 + 1/10 + 1/20 + 1/35.
a(20) = 77 = denominator of 115/77 = 1/1 + 1/4 + 1/10 + 1/20 + 1/35 + 1/56 + 1/84 + 1/120 + 1/165 + 1/220 + 1/286 + 1/364 + 1/455 + 1/560 + 1/680 + 1/816 + 1/969 + 1/1140 + 1/1330 + 1/1540.
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CROSSREFS
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Cf. A000292, A022998, A026741, A118391.
Sequence in context: A050017 A125514 A158320 this_sequence A130316 A131745 A151727
Adjacent sequences: A118389 A118390 A118391 this_sequence A118393 A118394 A118395
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KEYWORD
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easy,frac,nonn
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AUTHOR
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Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 27 2006
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