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Search: id:A118431
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| A118431 |
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Numerator of sum of reciprocals of first n 5-simplex numbers A000389. |
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+0
3
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| 1, 7, 17, 69, 625, 209, 329, 247, 357, 1250, 341, 1819, 2379, 3059, 19375, 1211, 1496, 3657, 4427, 53125, 12649, 14949, 17549, 10237, 59375, 6851, 7866, 35959, 40919, 231875, 52359, 14726, 16511, 36907, 205625, 91389, 101269
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OFFSET
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1,2
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COMMENT
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Denominators are A118432. Fractions are: 1/1, 7/6, 17/14, 69/56, 625/504, 209/168, 329/264, 247/198, 357/286, 1250/1001, 341/273, 1819/1456, 2379/1904, 3059/2448, 19375/15504, 1211/969, 1496/1197, 3657/2926, 4427/3542, 53125/42504, 12649/10120, 14949/11960, 17549/14040, 10237/8190, 59375/47502, 6851/5481, 7866/6293, 35959/28768, 40919/32736, 231875/185504, 52359/41888, 14726/11781, 16511/13209, 36907/29526, 205625/164502, 91389/73112, 101269/81016. The numerator of sum of reciprocals of first n triangular numbers is A026741. The numerator of sum of reciprocals of first n tetrahedral numbers is A118391. The numerator of sum of reciprocals of first n pentatope numbers is A118411.
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FORMULA
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A118411(n)/A118412(n) = SUM[i=1..n] (1/A000389(n)). A118411(n)/A118412(n) = SUM[i=1..n] (1/C(n,5)). A118411(n)/A118412(n) = SUM[i=1..n] (1/(n*(n+1)*(n+2)*(n+3)*(n+4)/120)).
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EXAMPLE
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a(1) = 1 = numerator of 1/1.
a(2) = 7 = numerator of 7/6 = 1/1 + 1/6.
a(3) = 17 = numerator of 17/14 = 1/1 + 1/6 + 1/21.
a(4) = 69 = numerator of 69/56 = 1/1 + 1/6 + 1/21 + 1/56.
a(5) = 55 = numerator of 55/42 = 1/1 + 1/6 + 1/21 + 1/56 + 1/126.
a(10) = 1250 = numerator of 1250/1001 = 1/1+ 1/6 + 1/21 + 1/56 + 1/126 + 1/252 + 1/462 + 1/792 + 1/1287 + 1/2002.
a(20) = 53125 = numerator of 53125/42504 = 1/1 + 1/6 + 1/21 + 1/56 + 1/126 + 1/252 + 1/462 + 1/792 + 1/1287 + 1/2002 + 1/3003 + 1/4368 + 1/6188 + 1/8568 + 1/11628 + 1/15504 + 1/20349 + 1/26334 + 1/33649 + 1/42504.
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CROSSREFS
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Cf. A000332, A000389, A022998, A026741, A118391, A118391, A118411, A118412, A118432.
Sequence in context: A081632 A106010 A136192 this_sequence A051809 A034054 A120876
Adjacent sequences: A118428 A118429 A118430 this_sequence A118432 A118433 A118434
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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 28 2006
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