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
Harry J. Smith, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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. - 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
Jason Earls, Jun 12 2001
EXTENSIONS
Better description and more terms from Larry Reeves (larryr(AT)acm.org), Jun 19 2001
STATUS
approved