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A128507 Denominators of partial sums for a series for 3*sqrt(2)*(Pi^3)/2^7. 4
1, 27, 3375, 1157625, 31255875, 41601569625, 91398648466125, 91398648466125, 449041559914072125, 3079976059450620705375, 439996579921517243625, 5353438387905100303185375, 669179798488137537898171875 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The numerators are given in A128506.

See the comments and the W. Lang link under A128506.

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..385

FORMULA

a(n) = denominator(r(n)) with the rationals r(n) = Sum_{k=0..n}(S(2*k,sqrt(2))/(2*k+1)^3 with Chebyshev's S-Polynomials S(2*k,sqrt(2))=[1,1,-1,-1] periodic sequence with period 4. See A057077.

EXAMPLE

Rationals r(n): [1, 28/27, 3473/3375, 1187864/1157625, 32115203/31255875,...].

3*sqrt(2)*(Pi^3)/2^7 = +1/1^3 +1/3^3 -1/5^3 -1/7^3 +1/9^3 +1/11^3 -1/13^3 -1/15^3 ++--

MATHEMATICA

r[n_]:= Sum[(1/2)*((1-I)*I^k+(1+I)*(-I)^k)/(2k+1)^3, {k, 0, n}]; Denominator[Table[r[n], {n, 0, 30}]] (* G. C. Greubel, Mar 28 2018

PROG

(PARI) {r(n) = sum(k=0, n, ((1-I)*I^k + (1+I)*(-I)^k)/(2*(2*k+1)^3))};

for(n=0, 30, print1(denominator(r(n)), ", ")) \\ G. C. Greubel, Mar 28 2018

CROSSREFS

Sequence in context: A226531 A017559 A069076 * A166750 A195374 A238698

Adjacent sequences:  A128504 A128505 A128506 * A128508 A128509 A128510

KEYWORD

nonn,frac,easy

AUTHOR

Wolfdieter Lang, Apr 04 2007

STATUS

approved

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Last modified May 23 03:10 EDT 2019. Contains 323507 sequences. (Running on oeis4.)