A370774 Denominator of the n-th partial sum of the generalized harmonic numbers A007406/A007407.
1, 4, 18, 144, 600, 3600, 44100, 78400, 635040, 254016, 12806640, 153679680, 1855133280, 8657288640, 16232416200, 519437318400, 8339854723200, 150117385017600, 541923759913536, 516117866584320
Offset: 1
Crossrefs
Cf. A120286 (numerators).
Programs
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Maple
A007406_7 := proc(n) local i; add(1/i^2,i=1..n) ; end proc: A370774 := proc(n) add( A007406_7(i),i=1..n) ; denom(%) ; end proc: seq(A370774(n),n=1..20) ;
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Mathematica
Table[-EulerGamma + HarmonicNumber[1 + n, 2] + n*HarmonicNumber[1 + n, 2] - PolyGamma[0, 2 + n], {n, 1, 20}] // Denominator (* Vaclav Kotesovec, May 02 2024 *) -
PARI
a(n) = denominator(sum(k=1, n, sum(i=1, k, 1/i^2))); \\ Michel Marcus, May 01 2024
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Python
from fractions import Fraction 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
Comments