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 A118412 Denominator of sum of reciprocals of first n pentatope numbers A000332. 4
 1, 5, 15, 105, 42, 63, 90, 495, 55, 143, 91, 1365, 420, 510, 612, 2907, 855, 665, 385, 1771, 1518, 1725, 1950, 8775, 2457, 5481, 1015, 4495, 1240, 4092, 4488, 19635, 5355, 11655, 6327, 9139, 2470, 2665, 8610, 37023 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Numerators are A118411. 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. LINKS FORMULA 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)). EXAMPLE a(1) = 1 = denominator of 1/1. a(2) = 5 = denominator of 6/5 = 1/1 + 1/5. a(3) = 15 = denominator of 19/15 = 1/1 + 1/5 + 1/15. a(4) = 105 = denominator of 136/105 = 1/1 + 1/5 + 1/15 + 1/35. a(5) = 42 = denominator of 55/42 = 1/1 + 1/5 + 1/15 + 1/35 + 1/70. a(10) = 143 = denominator of 190/143 = 1/1 + 1/5 + 1/15 + 1/35 + 1/70 + 1/126 + 1/210 + 1/330 + 1/495 + 1/715. a(20) = 1771 = denominator 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. PROG (PARI) s=0; for(i=4, 50, s+=1/binomial(i, 4); print(denominator(s))) /* Phil Carmody, Mar 27 2012 */ CROSSREFS Cf. A000332, A022998, A026741, A118391, A118391, A118411. Sequence in context: A292279 A268565 A121869 * A068622 A080449 A077702 Adjacent sequences:  A118409 A118410 A118411 * A118413 A118414 A118415 KEYWORD easy,frac,nonn AUTHOR Jonathan Vos Post, Apr 27 2006 STATUS approved

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Last modified April 21 10:03 EDT 2019. Contains 322328 sequences. (Running on oeis4.)