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%I #14 Sep 07 2024 01:14:24
%S 1,7,21,231,3003,3003,51051,969969,969969,22309287,111546435,
%T 334639305,9704539845,300840735195,300840735195,300840735195,
%U 11131107202215,11131107202215,456375395290815,19624141997505045,19624141997505045
%N a(n) = A111877(n+1)/5.
%H G. C. Greubel, <a href="/A111878/b111878.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = (1/15)*denominator(digamma(n+7/2)/2 + log(2) + euler_gamma/2).
%F a(n) = denominator(f(n+2)/15), where f(n) = Sum_{j=0..n} 1/(2*j+1).
%F a(n) = (1/15) * denominator of ( 2*H_{2*n+6} - H_{n+3} ), where H_{n} is the n-th Harmonic number. - _G. C. Greubel_, Jul 24 2023
%t With[{H=HarmonicNumber}, Table[Denominator[2*H[2*n+6] -H[n+3]]/15, {n, 0, 40}]] (* _G. C. Greubel_, Jul 24 2023 *)
%o (Magma) H:=HarmonicNumber; [Denominator((2*H(2*n+6) - H(n+3)))/15: n in [0..40]]; // _G. C. Greubel_, Jul 24 2023
%o (SageMath) h=harmonic_number; [denominator(2*h(2*n+6,1) - h(n+3,1))/15 for n in range(41)] # _G. C. Greubel_, Jul 24 2023
%Y Cf. A025547, A111877.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Aug 19 2005