The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
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!)
A027821 a(n) = 21*(n+1)*binomial(n+6,9). 1
84, 1050, 6930, 32340, 120120, 378378, 1051050, 2642640, 6126120, 13273260, 27159132, 52907400, 98760480, 177578940, 308897820, 521694096, 858049500, 1377926550, 2165313150, 3336032700, 5047562520, 7511253750, 11007400950, 15903669600, 22677454800, 31942814904 (list; graph; refs; listen; history; text; internal format)
OFFSET
3,1
COMMENTS
Number of 16-subsequences of [ 1, n ] with just 6 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
FORMULA
G.f.: 42*(2+3x)*x^3/(1-x)^11.
a(n) = C(n+1, 4)*C(n+6, 6). - Zerinvary Lajos, Jun 08 2005; corrected by R. J. Mathar, Feb 13 2016
From Amiram Eldar, Feb 03 2022: (Start)
Sum_{n>=3} 1/a(n) = 1161049/29400 - 4*Pi^2.
Sum_{n>=3} (-1)^(n+1)/a(n) = 2*Pi^2 - 1536*log(2)/35 + 104773/9800. (End)
MATHEMATICA
LinearRecurrence[{11, -55, 165, -330, 462, -462, 330, -165, 55, -11, 1}, {84, 1050, 6930, 32340, 120120, 378378, 1051050, 2642640, 6126120, 13273260, 27159132}, 30] (* Harvey P. Dale, Jul 07 2016 *)
CROSSREFS
Sequence in context: A093284 A027794 A219713 * A220049 A220210 A092719
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
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 May 28 12:54 EDT 2024. Contains 372913 sequences. (Running on oeis4.)