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A111877
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a(n) = denominator of 3*Sum_{j=0..n+1} 1/(2*j+1).
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3
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1, 5, 35, 105, 1155, 15015, 15015, 255255, 4849845, 4849845, 111546435, 557732175, 1673196525, 48522699225, 1504203675975, 1504203675975, 1504203675975, 55655536011075, 55655536011075, 2281876976454075, 98120709987525225
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OFFSET
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0,2
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LINKS
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FORMULA
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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
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MATHEMATICA
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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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PROG
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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
(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
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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