A118412 Denominator of sum of reciprocals of first n pentatope numbers A000332.

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

Offset: 1

Author

Jonathan Vos Post, Apr 27 2006

Keywords

• easy
• frac
• nonn

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.

Examples

			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.
		

Crossrefs

Cf. A000332, A022998, A026741, A118391, A118391, A118411.

Programs

PARI

s=0;for(i=4,50,s+=1/binomial(i,4);print(denominator(s))) /* Phil Carmody, Mar 27 2012 */

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)).