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A101627 Numerator of partial sums of a certain series. 5
1, 39, 241, 34883, 14039, 1516871, 7601151, 875425657, 7887002813, 7095769757767, 14199583385459, 75087685321529, 75113436870869, 927229349730873529, 927436191807263569, 305182576081725442901, 23479178371879154033, 37713848011377144613, 37717984058802320713, 135759786815564675620247 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The denominators are given in A101628.

Second member (m=3) of a family defined in A101028.

The limit s=lim(s(n),n->infinity) with the s(n) defined below equals 8*sum(zeta(2*k+1)/3^(2*k),k=1..infinity) with Euler's (or Riemann's) zeta function. This limit is 12*(log(3)-1) = 1.18334746...; see the Abramowitz-Stegun (given in A101028) reference p. 259, eq. 6.3.15 with z=1/3 together with p. 258.

LINKS

Table of n, a(n) for n=1..20.

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

Wolfdieter Lang, Rationals s(n) and more.

FORMULA

a(n)=numerator(s(n)) with s(n)=24*sum(1/((3*k-1)*(3*k)*(3*k+1)), k=1..n).

EXAMPLE

s(3)= 24*(1/(2*3*4)+ 1/(5*6*7) + 1/(8*9*10)) = 241/210, hence a(3)=241 and A101628(3)=210.

MATHEMATICA

Numerator[Accumulate[Table[8/(9k^3-k), {k, 20}]]]

PROG

(PARI) a(n) = numerator(24*sum(k=1, n, 1/((3*k-1)*(3*k)*(3*k+1))));

CROSSREFS

Cf. A101028 (m=2), A101629 (m=4), A101631 (m=5).

Cf. A101628 (denominators).

Sequence in context: A266104 A190538 A190606 * A229639 A070146 A327344

Adjacent sequences: A101624 A101625 A101626 * A101628 A101629 A101630

KEYWORD

nonn,frac,easy

AUTHOR

Wolfdieter Lang, Dec 23 2004

EXTENSIONS

More terms from Michel Marcus, Mar 01 2022

STATUS

approved

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Last modified November 30 12:40 EST 2022. Contains 358441 sequences. (Running on oeis4.)