OFFSET
0,2
FORMULA
G.f.: A(x) = 1/B(-x) where B(x) is the g.f. of A027307.
a(n) = (-1)^(n-1) * (1/n) * Sum_{k=0..n} binomial(n,k) * binomial(2*n+k-2,n-1) = (-1)^(n-1) * A108424(n) for n > 0.
D-finite with recurrence n*(2*n-1)*a(n) +3*(6*n^2-10*n+3)*a(n-1) +(-46*n^2+227*n-279)*a(n-2) +2*(n-3)*(2*n-7)*a(n-3)=0. - R. J. Mathar, Jul 25 2023
a(n) ~ c*(-1)^(n-1)*4^n*2F1([-n, 2*n-1], [n], -1)*n^(-3/2), with c = 1/(4*sqrt(Pi)) = A087197/4. - Stefano Spezia, Oct 21 2023
MAPLE
A364394 := proc(n)
if n = 0 then
1;
else
(-1)^(n-1)*add( binomial(n, k) * binomial(2*n+k-2, n-1), k=0..n)/n ;
end if;
end proc:
seq(A364394(n), n=0..80); # R. J. Mathar, Jul 25 2023
PROG
(PARI) a(n) = if(n==0, 1, (-1)^(n-1)*sum(k=0, n, binomial(n, k)*binomial(2*n+k-2, n-1))/n);
CROSSREFS
KEYWORD
sign
AUTHOR
Seiichi Manyama, Jul 22 2023
STATUS
approved