A119783 Numerator of Sum_{i=1..n} i^3/(n-i+1).

1, 17, 94, 965, 841, 6167, 18044, 225489, 75220, 4280111, 899494, 86645897, 26288822, 41914055, 296912584, 5893703327, 1703822073, 49486578079, 14076109870, 12725008135, 1190932611, 122366761563, 203957791852

Offset: 1

Author

Alexander Adamchuk, Jun 25 2006

Keywords

• frac
• nonn

Comments

Prime p divides a(2p-1), p>3. Prime p divides a(3p-1), p>2. Prime p divides a(p-1), p>3. p^2 divides a(p^2-1) for prime p>3. p^3 divides a(p^3-1) for prime p>3. p^4 divides a(p^4-1) for prime p>3. p^5 divides a(p^5-1) for p>3.

Crossrefs

Cf. A007406, A001008, A027612.

Programs

Mathematica

Numerator[Table[Sum[i^3/(n-i+1),{i,1,n}],{n,1,50}]]

Formula

a(n) = numerator( Sum_{i=1..n} i^3/(n-i+1) ).