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%I #17 Mar 20 2024 03:25:02
%S 1,1,12,3,45,18,560,2520,8400,225,207900,207900,840840,191100,7761600,
%T 50450400,15437822400,14034384,214885440,29331862560,645300976320,
%U 517068090,742096122768,463810076730,4466319257400,492206612040,68908925685600,11484820947600
%N Denominator of Sum_{k=1..n} H(k)*H(n+1-k), where H(k) is the k-th harmonic number (Sum_{j=1..k} 1/j).
%C A130894(n)/A130895(n) also equals 2*Sum_{k=1..n} H(k)*(n+1-k)/(k+1) = Sum_{k=1..n} H(2,k)/(n+1-k), where H(2,k) = Sum_{j=1..k} H(j) = (k+1)*H(k) - k.
%F A130894(n)/A130895(n) = (n+2)*(2 - 2*H(n+2) + (H(n+2))^2 - G(n+2)), where G(n) = Sum_{k=1..n} 1/k^2.
%t f[n_] := Sum[ HarmonicNumber[k] HarmonicNumber[n + 1 - k], {k, n}]; Table[ Denominator@ f@n, {n, 26}] (* _Robert G. Wilson v_, Jul 02 2007 *)
%Y Cf. A130894.
%K frac,nonn
%O 1,3
%A _Leroy Quet_, Jun 07 2007
%E More terms from _Robert G. Wilson v_, Jul 02 2007