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!)
A269877 A double binomial sum involving absolute values. 2
0, 8, 121728, 77214720, 12676235264, 1090372239360, 64922717257728, 3052335748087808, 121762580539637760, 4304417014325182464, 138706918527488491520, 4154140250223566389248, 117243264067548833906688, 3150495258536853477785600, 81236017376284183797694464 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
A fast algorithm follows from Theorem 5 of Brent et al. article.
LINKS
Richard P. Brent, Hideyuki Ohtsuka, Judy-anne H. Osborn, Helmut Prodinger, Some binomial sums involving absolute values, arXiv:1411.1477 [math.CO], 2016, page 11.
Index entries for linear recurrences with constant coefficients, signature (112,-5376,143360,-2293760,22020096,-117440512,268435456).
FORMULA
G.f.: 8*x*(1 + 15104*x + 7953024*x^2 + 585181184*x^3 + 8538456064*x^4 + 19750453248*x^5)/(1-16*x)^7.
a(n) = Sum_{k=-n..n} (Sum_{l=-n..n} binomial(2*n, n+k)*binomial(2*n, n+l)*(k^2 - l^2)^6).
a(n) = 2^(4*n-3)*n*(2*n-1)*(900*n^4-4500*n^3+8895*n^2-8055*n+2764).
MATHEMATICA
Table[2^(4 n - 3) n (2 n - 1) (900 n^4 - 4500 n^3 + 8895 n^2 - 8055 n + 2764), {n, 0, 15}]
LinearRecurrence[{112, -5376, 143360, -2293760, 22020096, -117440512, 268435456}, {0, 8, 121728, 77214720, 12676235264, 1090372239360, 64922717257728}, 20] (* Harvey P. Dale, Oct 28 2023 *)
PROG
(Magma) [2^(4*n-3)*n*(2*n-1)*(900*n^4-4500*n^3+8895*n^2-8055*n+2764): n in [0..20]];
CROSSREFS
Sequence in context: A259167 A048565 A339777 * A123276 A308138 A123651
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, May 10 2016
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 June 19 02:05 EDT 2024. Contains 373492 sequences. (Running on oeis4.)