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A074638
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Denominator of 1/3 + 1/7 + 1/11 + ... + 1/(4n-1).
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4
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3, 21, 231, 385, 7315, 168245, 4542615, 140821065, 28164213, 366134769, 15743795067, 739958368149, 12579292258533, 62896461292665, 3710891216267235, 3710891216267235, 248629711489904745, 17652709515783236895, 88263547578916184475, 6972820258734378573525
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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FORMULA
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Denominator( (Psi(n + 3/4) - Psi(3/4))/4 ). See the comment above. - Wolfdieter Lang, Apr 05 2022
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MATHEMATICA
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Table[ Denominator[ Sum[1/i, {i, 3/4, n}]], {n, 1, 20}]
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PROG
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(Python)
from fractions import Fraction
def a(n): return sum(Fraction(1, 4*i-1) for i in range(1, n+1)).denominator
(PARI) a(n) = denominator(sum(i=1, n, 1/(4*i-1))); \\ Michel Marcus, Mar 21 2021
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CROSSREFS
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The numerators times 4 are A074637.
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KEYWORD
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easy,frac,nonn
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AUTHOR
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STATUS
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approved
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