

A091528


Sum {k=1 to n} H(k) k! (nk)! (mod {n+1}), where H(k) is the kth harmonic number.


2



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
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OFFSET

1,4


LINKS

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


FORMULA

It appears that the sum {k=1 to n} H(k) k! (nk)! (mod {n+1}) 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], n!(1/2)HarmonicNumber[n/2], n!(HarmonicNumber[n]  (1/2)HarmonicNumber[ Floor[n/2]])]; Table[ Mod[ h[n], n + 1], {n, 1, 95}]
(* or the following for n > 2000 *) h[n_] := Block[{}, n! Sum[1/(2k  If[ EvenQ[n], 0, 1]), {k, 1, Floor[(n + 1)/2]}], n + 1]]


CROSSREFS

Cf. A091529, A091530.
Sequence in context: A077451 A019829 A200125 * A236679 A096392 A332964
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



