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A061550
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(2n+1)*(2n+3)*(2n+5).
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4
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15, 105, 315, 693, 1287, 2145, 3315, 4845, 6783, 9177, 12075, 15525, 19575, 24273, 29667, 35805, 42735, 50505, 59163, 68757, 79335, 90945, 103635, 117453, 132447, 148665, 166155, 184965, 205143, 226737, 249795, 274365, 300495, 328233, 357627
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| sum(1/a(k), k=0..n) = 1/12 - 1/((8*n+12)*(2*n+5)). Jolley equation 209 ( offset adjusted). [From Gary Detlefs, Sep 20 2011]
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REFERENCES
| L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 40
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0..1000
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| a(n) = A162540(n)/3.
1/15 + 1/105 + 1/315...= 1/12 [Jolley, eq. 209]
sum_{i=0..n-1} a(i) = A196506(n), partial sums [Jolley eq (43)] - R. J. Mathar, Mar 24 2011
sum_{i=0..infinity} (-1)^i/a(i) = Pi/8-1/3 = 0.0593657... [Jolley eq 240]
a(n)=(-1)^(n+1)*(4*n^2+12*n+7)/Integral_{x=0..Pi/2} (cos((2*n+3)*x))*(sin(x))^2 dx. [From Francesco Daddi, Aug 03 2011]
G.f. ( 15+45*x-15*x^2+3*x^3 ) / (x-1)^4 . - R. J. Mathar, Oct 03 2011
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MAPLE
| For n from 0 to 100 do (2*n+1)*(2*n+3)*(2*n+5) end do;
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MATHEMATICA
| f[n_] := n/GCD[n, 4]; Table[ f[n] f[n + 2] f[n + 4], {n, 1, 70, 2}] (* From Robert G. Wilson v, Jan 14 2011 *)
Times@@@(#+{1, 3, 5}&)/@(2Range[0, 35]) (* From Harvey P. Dale, Feb 13 2011 *)
Table[(2*n + 1)*(2*n + 3)*(2*n + 5), {n, 35}] (* T. D. Noe, Feb 13 2011 *)
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PROG
| (PARI) { for (n=0, 1000, write("b061550.txt", n, " ", (2*n + 1)*(2*n + 3)*(2*n + 5)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 24 2009]
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CROSSREFS
| Cf. A005408.
Sequence in context: A205424 A102791 A160892 * A174385 A185129 A090454
Adjacent sequences: A061547 A061548 A061549 * A061551 A061552 A061553
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KEYWORD
| easy,nonn
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AUTHOR
| Jason Earls (zevi_35711(AT)yahoo.com), Jun 12 2001
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EXTENSIONS
| Better description and more terms from Larry Reeves (larryr(AT)acm.org), Jun 19 2001
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