A111878 a(n) = A111877(n+1)/5.

1, 7, 21, 231, 3003, 3003, 51051, 969969, 969969, 22309287, 111546435, 334639305, 9704539845, 300840735195, 300840735195, 300840735195, 11131107202215, 11131107202215, 456375395290815, 19624141997505045, 19624141997505045

Offset: 0

Author

Paul Barry, Aug 19 2005

Keywords

• easy
• nonn

Links

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

Crossrefs

Cf. A025547, A111877.

Programs

Magma

H:=HarmonicNumber; [Denominator((2*H(2*n+6) - H(n+3)))/15: n in [0..40]]; // G. C. Greubel, Jul 24 2023

Mathematica

With[{H=HarmonicNumber}, Table[Denominator[2*H[2*n+6] -H[n+3]]/15, {n, 0, 40}]] (* G. C. Greubel, Jul 24 2023 *)

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

Formula

a(n) = (1/15)*denominator(digamma(n+7/2)/2 + log(2) + euler_gamma/2).

a(n) = denominator(f(n+2)/15), where f(n) = Sum_{j=0..n} 1/(2*j+1).

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