A120487 Denominator of 1^n/n + 2^n/(n-1) + 3^n/(n-2) + ... + (n-1)^n/2 + n^n/1.

1, 2, 3, 12, 5, 20, 35, 280, 63, 2520, 385, 27720, 6435, 8008, 45045, 720720, 85085, 4084080, 969969, 739024, 29393, 5173168, 7436429, 356948592, 42902475, 2974571600, 717084225, 80313433200, 215656441, 2329089562800, 4512611027925

Offset: 1

Author

Alexander Adamchuk, Jul 22 2006

Keywords

• frac
• nonn

Comments

Numerator is A115071(n).

Also a(n) is denominator of (n+1)^(n+1) * (H(n+1) - 1), where H(k) is harmonic number, H(k) = Sum_{i=1..k} 1/i = A001008(k)/A002805(k). - Alexander Adamchuk, Jan 02 2007

Crossrefs

Cf. A115071, A027612, A031971, A002805.

Cf. A001008, A002805.

Programs

Mathematica

Denominator[Table[Sum[k^n/(n-k+1),{k,1,n}],{n,1,50}]]
Table[ Denominator[ (n+1)^(n+1) * Sum[ 1/i,{i,2,n+1} ] ], {n,1,40} ] (* Alexander Adamchuk, Jan 02 2007 *)

Formula

a(n) = denominator(Sum_{k=1..n} k^n/(n-k+1)).

a(n) = denominator((n+1)^(n+1) * Sum_{i=2..n+1} 1/i). - Alexander Adamchuk, Jan 02 2007