OFFSET
0,3
FORMULA
From Petros Hadjicostas, Dec 03 2017: (Start)
a(n) = (1/(2*n+5))*Sum_{d|gcd(n,5)} mu(d)*binomial((2*n+5)/d, n/d). (This is a special case of A. Howroyd's formula for double array A051168.)
a(n) = (1/(2*n+5))*(binomial(2*n+5, n) - binomial((2*n/5)+1, n/5)) if 5|n; = (1/(2*n+5))*binomial(2*n+5, n) otherwise.
(End)
MAPLE
A050183 := proc(n)
binomial(2*n+5, n) ;
if modp(n, 5) = 0 then
%-binomial(2*n/5+1, n/5) ;
end if;
%/(2*n+5) ;
end proc:
seq(A050183(n), n=0..40) ; # R. J. Mathar, Oct 28 2021
PROG
(PARI) a(n) = (1/(2*n+5))*sumdiv(gcd(n, 5), d, moebius(d)*binomial((2*n+5)/d, n/d)); \\ Michel Marcus, Dec 05 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved