A111876 Denominator of Sum_{k = 0..n} 1/((k+1)*(2*k+1)).

1, 6, 30, 420, 1260, 13860, 180180, 72072, 1225224, 116396280, 116396280, 2677114440, 13385572200, 5736673800, 166363540200, 10314539492400, 10314539492400, 72201776446800, 2671465728531600, 2671465728531600

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = denominator of ( digamma(n+3/2) - digamma(n+2) + 2*log(2) ).

a(n) = denominator of 2*(n+1)*Integral_{x = 0..1} x^n* log(1+sqrt(x)) dx.

a(n-1) = denominator( (1/n)*Sum_{k = 1..n} (n - k)/(n + k) ). - Peter Bala, Oct 10 2021

Maple

seq(denom( add(1/((k+1)*(2*k+1)), k = 0..n) ), n = 0..20); # Peter Bala, Oct 10 2021

Mathematica

Table[Denominator[HarmonicNumber[2n+2] - HarmonicNumber[n+1]]/2, {n, 0, 30}]

Prog

(PARI) a(n) = denominator(sum(k=0, n, 1/((k+1)*(2*k+1)))); \\ Michel Marcus, Oct 10 2021
(Magma) [Denominator(HarmonicNumber(2*n+2) -HarmonicNumber(n+1))/2: n in [0..40]]; // G. C. Greubel, Jul 24 2023
(SageMath) [denominator(harmonic_number(2*n+2, 1) - harmonic_number(n+1, 1))/2 for n in range(41)] # G. C. Greubel, Jul 24 2023

Crossrefs

Cf. A082687 (numerators), A117664.

Sequence in context: A332041 A201135 A369135 * A119634 A256545 A349981

Adjacent sequences: A111873 A111874 A111875 * A111877 A111878 A111879

Keyword

easy,nonn,frac

Author

Paul Barry, Aug 19 2005

Status

approved