OFFSET
0,2
COMMENTS
A fast algorithm follows from Lemma 1 of Brent et al. article.
LINKS
Richard P. Brent, Hideyuki Ohtsuka, Judy-anne H. Osborn, Helmut Prodinger, Some binomial sums involving absolute values, arXiv:1411.1477v2 [math.CO], 2016.
FORMULA
a(n) = Sum_{k=-n..n} (Sum_{l=-n..n} binomial(2*n, n+k)*binomial(2*n, n+l)*abs(k^2 - l^2)^3).
Conjecture D-finite with recurrence -(4621*n-8921)*(n-1)^2*a(n) +4*(148256*n^3 -1055204*n^2 +2794799*n -2529792)*a(n-1) -64*(32443*n- 32400)*(2*n-3)*(2*n-5)*a(n-2)=0. - R. J. Mathar, Feb 27 2023
MAPLE
A268150 := proc(n)
add( add( binomial(2*n, n+k)*binomial(2*n, n+l)*abs(k^2-l^2)^3, l=-n..n), k=-n..n) ;
end proc:
seq(A268150(n), n=0..10) ; # R. J. Mathar, Feb 27 2023
PROG
(PARI) a(n) = sum(k=-n, n, sum(l=-n, n, binomial(2*n, n+k)*binomial(2*n, n+l)*abs(k^2 - l^2)^3));
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Richard P. Brent, Jan 27 2016
STATUS
approved