This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A091528 #17 Jul 11 2025 08:49:05
%S A091528 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,
%T A091528 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,
%U A091528 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
%N A091528 a(n) = (Sum_{k=1..n} H(k)*k!*(n-k)!) mod (n+1), where H(k) is the k-th harmonic number.
%F A091528 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.
%t A091528 Table[ Mod[ Sum[ HarmonicNumber[k]k!(n - k)!, {k, 1, n}], n + 1], {n, 1, 95}] (* or *) (* _Robert G. Wilson v_, Jan 14 2004 *)
%t A091528 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}]
%t A091528 (* 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}]
%Y A091528 Cf. A091529, A091530.
%K A091528 nonn
%O A091528 1,4
%A A091528 _Leroy Quet_, Jan 08 2004
%E A091528 Edited and extended by _Robert G. Wilson v_, Jan 14 2004