OFFSET
0,5
FORMULA
a(n)=sum{k=0..n, if(mod(n-k,3)=1, (1/n)*C(n,k)*C(n,k+1), 0)}
a(0)=0, a(n)=sum{k=0..floor(n/3), (1/n)*C(n,3k+1)C(n,3k)},n>0; - Paul Barry, Jan 25 2007
Conjecture D-finite with recurrence +n*(881*n-4580)*(n-2)*(n+1)*a(n) -3*n*(612*n^3-2827*n^2-2988*n+10135)*a(n-1) +3*(-3088*n^4+42803*n^3-190361*n^2+313702*n-167988)*a(n-2) +(43042*n^4-600920*n^3+2924411*n^2-5860777*n+4115562)*a(n-3) +3*(-38600*n^4+558681*n^3-2904370*n^2+6389913*n-4965528)*a(n-4) +3*(-14776*n^4+162695*n^3-434711*n^2-415064*n+1878084)*a(n-5) -9*(n-6)*(10835*n^3-106831*n^2+290611*n-173519)*a(n-6) +54*(n-6)*(n-7)*(593*n-1429)*(2*n-13)*a(n-7)=0. - R. J. Mathar, Feb 03 2025
MAPLE
A119366 := proc(n)
if n = 0 then
0;
else
add(binomial(n, 3*k+1)*binomial(n, 3*k), k=0..n/3) ;
%/n ;
end if;
end proc: # R. J. Mathar, Dec 02 2014
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 16 2006
STATUS
approved