A118431 Numerator of sum of reciprocals of first n 5-simplex numbers A000389.

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

Offset: 1

Author

Jonathan Vos Post, Apr 28 2006

Keywords

• easy
• frac
• nonn

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.

Examples

			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.
		

Links

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

Crossrefs

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

Programs

Mathematica

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

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)).