A115071 Numerator of 1^n/n + 2^n/(n-1) + 3^n/(n-2) +...+ (n-1)^n/2 + n^n/1.

1, 9, 94, 3625, 18631, 1120581, 34793764, 5692787001, 29669041771, 30708223774261, 134127439064434, 302304605103335861, 2387352152511746837, 109134149200789179825, 24217460586461892638584

Offset

1,2

Comments

a(p-1) is divisible by p^3 for prime p>3. a(p^2-1) is divisible by p^6 for prime p>3. a(p^3-1) is divisible by p^9 for prime p>3.

Links

Table of n, a(n) for n=1..15.

Formula

a(n) = numerator(Sum_{i=1..n} i^n/(n+1-i)).

Example

a(1) = numerator(1/1) = 1.
a(2) = numerator(1/2 + 4/1) = 9.
a(3) = numerator(1/3 + 8/2 + 27/1) = 94.
a(4) = numerator(1/4 + 16/3 + 81/2 + 256/1) = 3625.

Mathematica

Table[Numerator[Sum[i^n/(n+1-i), {i, 1, n}]], {n, 1, 20}]

Crossrefs

Cf. A001008, A027612, A120487 (denominator).

Sequence in context: A307961 A099297 A057782 * A000562 A193216 A213019

Adjacent sequences: A115068 A115069 A115070 * A115072 A115073 A115074

Keyword

frac,nonn,easy

Author

Alexander Adamchuk, Jun 17 2006

Status

approved