login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A069080 a(n) = (2n+1)*(2n+2)*(2n+6)*(2n+7). 1
84, 864, 3300, 8736, 18900, 35904, 62244, 100800, 154836, 228000, 324324, 448224, 604500, 798336, 1035300, 1321344, 1662804, 2066400, 2539236, 3088800, 3722964, 4449984, 5278500, 6217536, 7276500, 8465184, 9793764, 11272800, 12913236, 14726400, 16724004 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
Konrad Knopp, Theory and application of infinite series, Dover, p. 268.
LINKS
Konrad Knopp, Theorie und Anwendung der unendlichen Reihen, Berlin, J. Springer, 1922. (Original german edition of "Theory and Application of Infinite Series")
FORMULA
Sum_{n>=0} (-1)^n/a(n) = (Pi-149/60)/60. [Corrected by Amiram Eldar, Mar 08 2022]
From Wesley Ivan Hurt, Mar 28 2015: (Start)
G.f.: 12*(7 + 37*x - 15*x^2 + 3*x^3) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
a(n) = 16*n^4 + 128*n^3 + 332*n^2 + 304*n + 84. (End)
Sum_{n>=0} 1/a(n) = 49/3600. - Amiram Eldar, Mar 08 2022
MAPLE
A069080:=n->16*n^4 + 128*n^3 + 332*n^2 + 304*n + 84: seq(A069080(n), n=0..30); # Wesley Ivan Hurt, Mar 28 2015
MATHEMATICA
CoefficientList[Series[12 (7 + 37x - 15x^2 + 3x^3)/(1 - x)^5, {x, 0, 30}], x] (* Wesley Ivan Hurt, Mar 28 2015 *)
PROG
(Magma) [(2*n+1)*(2*n+2)*(2*n+6)*(2*n+7) : n in [0..30]]; // Wesley Ivan Hurt, Mar 28 2015
(PARI) Vec(12*(7 + 37*x - 15*x^2 + 3*x^3) / (1 - x)^5 + O(x^50)) \\ Michel Marcus, Mar 29 2015
(PARI) vector(50, n, n--; (2*n+1)*(2*n+2)*(2*n+6)*(2*n+7)) \\ Michel Marcus, Mar 29 2015
CROSSREFS
Sequence in context: A220016 A219827 A219719 * A219577 A093284 A027794
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Apr 05 2002
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 21 01:34 EDT 2024. Contains 371850 sequences. (Running on oeis4.)