The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A091528 Sum {k=1 to n} H(k) k! (n-k)! (mod {n+1}), where H(k) is the k-th 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 LINKS FORMULA It appears that the sum {k=1 to n} H(k) k! (n-k)! (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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified April 3 04:21 EDT 2020. Contains 333195 sequences. (Running on oeis4.)