OFFSET
0,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: 1 / ( sqrt(1-4*x) * (1 - x * c(x)^4) ), where c(x) is the g.f. of A000108.
D-finite with recurrence +n*(n-7)*a(n) -(7*n-4)*(n-7)*a(n-1) +4*(n^2-13*n+17)*a(n-2) +(35*n^2-217*n+304)*a(n-3) -2*(n-2)*(7*n-29)*a(n-4) +4*(n-2)*(2*n-9)*a(n-5)=0. - R. J. Mathar, Mar 12 2023
MAPLE
A360143 := proc(n)
add(binomial(2*n+2*k, n-k), k=0..n) ;
end proc:
seq(A360143(n), n=0..70) ; # R. J. Mathar, Mar 12 2023
PROG
(PARI) a(n) = sum(k=0, n, binomial(2*n+2*k, n-k));
(PARI) my(N=30, x='x+O('x^N)); Vec(1/(sqrt(1-4*x)*(1-x*(2/(1+sqrt(1-4*x)))^4)))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Jan 27 2023
STATUS
approved