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%I #7 Apr 25 2016 11:45:29
%S 1,6,19,136,83,119,656,73,190,121,1816,559,679,815,3872,1139,886,513,
%T 2360,2023,2299,2599,11696,3275,7306,1353,5992,1653,5455,5983,26176,
%U 7139,15538,8435,12184,3293,3553,11479,49360
%N Numerator of sum of reciprocals of first n pentatope numbers A000332.
%C Denominators are A118412. Fractions are: 1/1, 6/5, 19/15, 136/105, 83/63, 119/90, 656/495, 73/55, 190/143, 121/91, 1816/1365, 559/420, 679/510, 815/612, 3872/2907, 1139/855, 886/665, 513/385, 2360/1771, 2023/1518, 2299/1725, 2599/1950, 11696/8775, 3275/2457, 7306/5481, 1353/1015, 5992/4495, 1653/1240, 5455/4092, 5983/4488, 26176/19635, 7139/5355, 15538/11655, 8435/6327, 12184/9139, 3293/2470, 3553/2665, 11479/8610, 49360/37023. The denominator of sum of reciprocals of first n triangular numbers is A026741. The denominator of sum of reciprocals of first n tetrahedral numbers is A118392.
%F A118411(n)/A118412(n) = SUM[i=1..n] (1/A000332(n)). A118411(n)/A118412(n) = SUM[i=1..n] (1/C(n+2,4)). A118411(n)/A118412(n) = SUM[i=1..n] (1/(n*(n+1)*(n+2)*(n+3)/24)).
%e a(1) = 1 = numerator of 1/1.
%e a(2) = 6 = numerator of 6/5 = 1/1 + 1/5.
%e a(3) = 19 = numerator of 19/15 = 1/1 + 1/5 + 1/15.
%e a(4) = 136 = numerator of 136/105 = 1/1 + 1/5 + 1/15 + 1/35.
%e a(5) = 55 = numerator of 55/42 = 1/1 + 1/5 + 1/15 + 1/35 + 1/70.
%e a(10) = 190 = numerator of 190/143 = 1/1 + 1/5 + 1/15 + 1/35 + 1/70 + 1/126 + 1/210 + 1/330 + 1/495 + 1/715.
%e a(20) = 2360 = numerator of 2360/1771 = 1/1 + 1/5 + 1/15 + 1/35 + 1/70 + 1/126 + 1/210 + 1/330 + 1/495 + 1/715 + 1/1001 + 1/1365 + 1/1820 + 1/2380 + 1/3060 + 1/3876 + 1/4845 + 1/5985 + 1/7315 + 1/8855.
%o (PARI) s=0;for(i=4,50,s+=1/binomial(i,4);print(numerator(s))) /* Phil Carmody, Mar 27 2012 */
%Y Cf. A000332, A022998, A026741, A118391, A118391, A118412.
%K easy,frac,nonn
%O 1,2
%A _Jonathan Vos Post_, Apr 27 2006
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