A074638 Denominator of 1/3 + 1/7 + 1/11 + ... + 1/(4n-1).

3, 21, 231, 385, 7315, 168245, 4542615, 140821065, 28164213, 366134769, 15743795067, 739958368149, 12579292258533, 62896461292665, 3710891216267235, 3710891216267235, 248629711489904745, 17652709515783236895, 88263547578916184475, 6972820258734378573525

Offset: 1

Author

Robert G. Wilson v, Aug 27 2002

Keywords

• easy
• frac
• nonn

Comments

This s(n) := Sum_{j=0..n-1} 1/(4*j + 3), for n >= 1, equals (Psi(n + 3/4) - Psi(3/4))/4, with the digamma function Psi(z). See Abramowitz-Stegun, p. 258, eqs. 6.3.7 and 6.3.5, with z -> 3/4. A200134 = -Psi(3/4). - Wolfdieter Lang, Apr 06 2022

Links

• Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions. p.258, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. p. 258.

Crossrefs

The numerators times 4 are A074637.

Cf. A075135, A200134.

Programs

Mathematica

Table[ Denominator[ Sum[1/i, {i, 3/4, n}]], {n, 1, 20}]

PARI

a(n) = denominator(sum(i=1, n, 1/(4*i-1))); \\ Michel Marcus, Mar 21 2021

Python

from fractions import Fraction
def a(n): return sum(Fraction(1, 4*i-1) for i in range(1, n+1)).denominator
print([a(n) for n in range(1, 21)]) # Michael S. Branicky, Mar 21 2021

Formula

Denominator( (Psi(n + 3/4) - Psi(3/4))/4 ). See the comment above. - Wolfdieter Lang, Apr 05 2022