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URL: https://oeis.org/A111876

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A111876
Denominator of Sum_{k = 0..n} 1/((k+1)*(2*k+1)).
4
1, 6, 30, 420, 1260, 13860, 180180, 72072, 1225224, 116396280, 116396280, 2677114440, 13385572200, 5736673800, 166363540200, 10314539492400, 10314539492400, 72201776446800, 2671465728531600, 2671465728531600
OFFSET
0,2
LINKS
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
KEYWORD
easy,nonn,frac
AUTHOR
Paul Barry, Aug 19 2005
STATUS
approved