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
Keywords
Programs
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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}]
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.
Extensions
Edited and extended by Robert G. Wilson v, Jan 14 2004