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A118431 Numerator of sum of reciprocals of first n 5-simplex numbers A000389. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

FORMULA

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)).

EXAMPLE

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.

MATHEMATICA

Numerator[Accumulate[1/Binomial[Range[5, 50], 5]]] (* G. C. Greubel, Nov 21 2017 *)

CROSSREFS

Cf. A000332, A000389, A022998, A026741, A118391, A118391, A118411, A118412, A118432.

Sequence in context: A106010 A136192 A269239 * A051809 A254500 A242907

Adjacent sequences:  A118428 A118429 A118430 * A118432 A118433 A118434

KEYWORD

easy,frac,nonn

AUTHOR

Jonathan Vos Post, Apr 28 2006

STATUS

approved

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Last modified May 16 23:46 EDT 2021. Contains 343957 sequences. (Running on oeis4.)