A119782 Numerator of Sum[ i^3/(n-i+1)^2, {i,1,n}].

1, 33, 262, 10325, 7227, 923027, 4588732, 49631229, 29087285, 1618749187, 152762993, 69307256941, 191848206263, 702044812445, 9181629908344, 2873944084323677, 1547933530301469, 1198197057199579439

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = numerator[ Sum[i^3/(n-i+1)^2, {i,1,n}]].

Mathematica

Numerator[Table[Sum[i^3/(n-i+1)^2, {i, 1, n}], {n, 1, 50}]]

Crossrefs

Cf. A007406, A001008, A027612.

Sequence in context: A344524 A197398 A061223 * A252978 A268264 A008515

Adjacent sequences: A119779 A119780 A119781 * A119783 A119784 A119785

Keyword

frac,nonn

Author

Alexander Adamchuk, Jun 25 2006

Status

approved