A091528 a(n) = (Sum_{k=1..n} H(k)*k!*(n-k)!) mod (n+1), where H(k) is the k-th harmonic number.

1, 1, 0, 3, 4, 2, 0, 6, 6, 5, 0, 3, 8, 0, 0, 13, 0, 3, 0, 0, 12, 17, 0, 0, 14, 0, 0, 1, 0, 6, 0, 0, 18, 0, 0, 1, 20, 0, 0, 23, 0, 25, 0, 0, 24, 44, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 30, 8, 0, 36, 32, 0, 0, 0, 0, 10, 0, 0, 0, 2, 0, 56, 38, 0, 0, 0, 0, 19, 0, 0, 42, 48, 0, 0, 44, 0, 0, 6, 0, 0, 0, 0, 48, 0, 0

Offset

1,4

Links

Table of n, a(n) for n=1..95.

Formula

It appears that a(n) is congruent to n!*h(n) (mod {n+1}) where h(n) = (1/2)*H(n/2) for even n and h(n) = H(n) - (1/2)*H(floor(n/2)) for odd n.

Mathematica

Table[ Mod[ Sum[ HarmonicNumber[k]k!(n - k)!, {k, 1, n}], n + 1], {n, 1, 95}] (* or *) (* Robert G. Wilson v, Jan 14 2004 *)
h[n_] := If[ EvenQ[n], (1/2)HarmonicNumber[n/2], HarmonicNumber[n] - (1/2)HarmonicNumber[ Floor[n/2]]]; Table[ Mod[ n!h[n], n + 1], {n, 1, 95}]
(* or *) h[n_] := Sum[1/(2k - If[ EvenQ[n], 0, 1]), {k, 1, Floor[(n + 1)/2]}]; Table[ Mod[ n!h[n], n + 1], {n, 1, 95}]

Crossrefs

Cf. A001008/A002805, A091529, A091530.

Sequence in context: A383115 A384782 A200125 * A236679 A364871 A096392

Adjacent sequences: A091525 A091526 A091527 * A091529 A091530 A091531

Keyword

nonn

Author

Leroy Quet, Jan 08 2004

Extensions

Edited and extended by Robert G. Wilson v, Jan 14 2004

Status

approved