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%I #17 Jun 09 2024 23:58:54
%S 1,4,18,144,600,3600,44100,78400,635040,254016,12806640,153679680,
%T 1855133280,8657288640,16232416200,519437318400,8339854723200,
%U 150117385017600,541923759913536,516117866584320
%N Denominator of the n-th partial sum of the generalized harmonic numbers A007406/A007407.
%C Partial sums of A007406/A007407 are 1, 9/4, 65/18, 725/144, 3899/600, 28763/3600, ...
%p A007406_7 := proc(n)
%p local i;
%p add(1/i^2,i=1..n) ;
%p end proc:
%p A370774 := proc(n)
%p add( A007406_7(i),i=1..n) ;
%p denom(%) ;
%p end proc:
%p seq(A370774(n),n=1..20) ;
%t Table[-EulerGamma + HarmonicNumber[1 + n, 2] + n*HarmonicNumber[1 + n, 2] - PolyGamma[0, 2 + n], {n, 1, 20}] // Denominator (* _Vaclav Kotesovec_, May 02 2024 *)
%o (PARI) a(n) = denominator(sum(k=1, n, sum(i=1, k, 1/i^2))); \\ _Michel Marcus_, May 01 2024
%o (Python)
%o from fractions import Fraction
%o def A370774(n): return sum(Fraction(n-i+1,i**2) for i in range(1,n+1)).denominator # _Chai Wah Wu_, May 01 2024
%Y Cf. A120286 (numerators).
%K nonn,frac,easy
%O 1,2
%A _R. J. Mathar_, May 01 2024
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