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

0,2

Links

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

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

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 *)

Prog

(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

Crossrefs

Cf. A001620, A025547, A350669 (numerators).

Sequence in context: A090294 A162540 A161199 * A179337 A053126 A096743

Adjacent sequences: A111874 A111875 A111876 * A111878 A111879 A111880

Keyword

easy,nonn

Author

Paul Barry, Aug 19 2005

Extensions

Name edited by G. C. Greubel, Jul 24 2023

Status

approved