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

1,2

Comments

Partial sums of A007406/A007407 are 1, 9/4, 65/18, 725/144, 3899/600, 28763/3600, ...

Links

Table of n, a(n) for n=1..20.

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) ;

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 *)

Prog

(PARI) a(n) = denominator(sum(k=1, n, sum(i=1, k, 1/i^2))); \\ Michel Marcus, May 01 2024
(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

Crossrefs

Cf. A120286 (numerators).

Sequence in context: A214647 A156445 A304997 * A060841 A059837 A220266

Adjacent sequences: A370771 A370772 A370773 * A370775 A370776 A370777

Keyword

nonn,frac,easy

Author

R. J. Mathar, May 01 2024

Status

approved