|
|
A061550
|
|
a(n) = (2n+1)*(2n+3)*(2n+5).
|
|
6
|
|
|
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;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
sum(1/a(k), k=0..n) = 1/12 - 1/((8*n+12)*(2*n+5)). Jolley equation 209 (offset adjusted). - Gary Detlefs, Sep 20 2011
|
|
REFERENCES
|
L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 40
|
|
LINKS
|
|
|
FORMULA
|
1/15 + 1/105 + 1/315...= 1/12 [Jolley, eq. 209]
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. - 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
|
|
MAPLE
|
For n from 0 to 100 do (2*n+1)*(2*n+3)*(2*n+5) end do;
|
|
MATHEMATICA
|
f[n_] := n/GCD[n, 4]; Table[ f[n] f[n + 2] f[n + 4], {n, 1, 70, 2}] (* Robert G. Wilson v, Jan 14 2011 *)
Times@@@(#+{1, 3, 5}&)/@(2Range[0, 35]) (* Harvey P. Dale, Feb 13 2011 *)
Table[(2*n + 1)*(2*n + 3)*(2*n + 5), {n, 35}] (* T. D. Noe, Feb 13 2011 *)
|
|
PROG
|
(PARI) { for (n=0, 1000, write("b061550.txt", n, " ", (2*n + 1)*(2*n + 3)*(2*n + 5)) ) } \\ Harry J. Smith, Jul 24 2009
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Better description and more terms from Larry Reeves (larryr(AT)acm.org), Jun 19 2001
|
|
STATUS
|
approved
|
|
|
|