A111877 a(n) = denominator of 3*Sum_{j=0..n+1} 1/(2*j+1).
1, 5, 35, 105, 1155, 15015, 15015, 255255, 4849845, 4849845, 111546435, 557732175, 1673196525, 48522699225, 1504203675975, 1504203675975, 1504203675975, 55655536011075, 55655536011075, 2281876976454075, 98120709987525225
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
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Magma
[Denominator((2*HarmonicNumber(2*n+4) - HarmonicNumber(n+2)))/3: n in [0..40]]; // G. C. Greubel, Jul 24 2023
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Mathematica
f[x_]:= 2*x+1; a[1]= f[1]; a[n_]:= LCM[f[n], a[n-1]]; Array[a, 21]/3 (* Robert G. Wilson v, Jan 04 2013 *)
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SageMath
[denominator(2*harmonic_number(2*n+4,1) - harmonic_number(n+2,1))/3 for n in range(41)] # G. C. Greubel, Jul 24 2023
Formula
a(n) = denominator of (3/2)*(digamma(n+5/2) + 2*log(2) + euler_gamma).
a(n) = denominator of ( 3*Sum_{j=0..n+1} 1/(2*j+1) ).
a(n) = (1/3) * denominator of ( 2*H_{2*n+4} - H_{n+2} ), where H_{n} is the n-th Harmonic number. - G. C. Greubel, Jul 24 2023
Extensions
Name edited by G. C. Greubel, Jul 24 2023