This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A118431 #6 Nov 21 2017 18:21:52
%S A118431 1,7,17,69,625,209,329,247,357,1250,341,1819,2379,3059,19375,1211,
%T A118431 1496,3657,4427,53125,12649,14949,17549,10237,59375,6851,7866,35959,
%U A118431 40919,231875,52359,14726,16511,36907,205625,91389,101269
%N A118431 Numerator of sum of reciprocals of first n 5-simplex numbers A000389.
%C A118431 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.
%H A118431 G. C. Greubel, <a href="/A118431/b118431.txt">Table of n, a(n) for n = 1..5000</a>
%F A118431 A118411(n)/A118412(n) = Sum_{i=1..n} (1/A000389(n)).
%F A118431 A118411(n)/A118412(n) = Sum_{i=1..n} (1/C(n,5)).
%F A118431 A118411(n)/A118412(n) = Sum_{i=1..n} (1/(n*(n+1)*(n+2)*(n+3)*(n+4)/120)).
%e A118431 a(1) = 1 = numerator of 1/1.
%e A118431 a(2) = 7 = numerator of 7/6 = 1/1 + 1/6.
%e A118431 a(3) = 17 = numerator of 17/14 = 1/1 + 1/6 + 1/21.
%e A118431 a(4) = 69 = numerator of 69/56 = 1/1 + 1/6 + 1/21 + 1/56.
%e A118431 a(5) = 55 = numerator of 55/42 = 1/1 + 1/6 + 1/21 + 1/56 + 1/126.
%e A118431 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.
%e A118431 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.
%t A118431 Numerator[Accumulate[1/Binomial[Range[5, 50], 5]]] (* _G. C. Greubel_, Nov 21 2017 *)
%Y A118431 Cf. A000332, A000389, A022998, A026741, A118391, A118391, A118411, A118412, A118432.
%K A118431 easy,frac,nonn
%O A118431 1,2
%A A118431 _Jonathan Vos Post_, Apr 28 2006