1,2

Numerators are A118431. 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 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. The denominator of sum of reciprocals of first n pentatope numbers is A118412.

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)).

a(1) = 1 = denominator of 1/1.

a(2) = 6 = denominator of 7/6 = 1/1 + 1/6.

a(3) = 14 = denominator of 17/14 = 1/1 + 1/6 + 1/21.

a(4) = 56 = denominator of 69/56 = 1/1 + 1/6 + 1/21 + 1/56.

a(5) = 42 = denominator of 55/42 = 1/1 + 1/6 + 1/21 + 1/56 + 1/126.

a(10) = 1001 = denominator 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) = 42504 = denominator 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.

Cf. A000332, A000389, A022998, A026741, A118391, A118391, A118411, A118412, A118431.

Adjacent sequences: A118429 A118430 A118431 this_sequence A118433 A118434 A118435

Sequence in context: A005515 A114705 A107301 this_sequence A032404 A059954 A139257

easy,frac,nonn

Jonathan Vos Post (jvospost3(AT)gmail.com), Apr 28 2006