OFFSET
0,3
FORMULA
a(n) = (-1)^n * Sum_{k=0..n} (-2)^k * binomial(n,k) * binomial(n+3*k+1,n) / (n+3*k+1).
D-finite with recurrence 3*n*(3*n-1)*(3*n+1)*a(n) +(-566*n^3 +1335*n^2 -1105*n +312)*a(n-1) +3*(943*n^3 -5739*n^2 +11016*n -6748)*a(n-2) +18*(-250*n^3 +2499*n^2 -8233*n +8938)*a(n-3) +27*(n-4)*(31*n^2 -314*n +735)*a(n-4) +81*(10*n -51)*(n-4) *(n-5)*a(n-5) +243*(n-5) *(n-6)*(n-4)*a(n-6)=0. - R. J. Mathar, Jul 25 2023
MAPLE
A364430 := proc(n)
(-1)^n*add((-2)^k* binomial(n, k) * binomial(n+3*k+1, n) / (n+3*k+1), k=0..n) ;
end proc:
seq(A364430(n), n=0..70); # R. J. Mathar, Jul 25 2023
PROG
(PARI) a(n) = (-1)^n*sum(k=0, n, (-2)^k*binomial(n, k)*binomial(n+3*k+1, n)/(n+3*k+1));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jul 24 2023
STATUS
approved