A298567 a(n) = Sum_{k=0..2*n/3} C(n-k,2*k-n)^2.

1, 0, 1, 1, 1, 4, 2, 9, 10, 17, 37, 41, 102, 136, 251, 450, 667, 1325, 2011, 3658, 6246, 10293, 18686, 30461, 54183, 92169, 157438, 276414, 466579, 818256, 1400509, 2419379, 4202829, 7208342, 12556360, 21621891, 37480728, 64965461, 112227269

Offset: 0

Author

Vladimir Kruchinin, Jan 21 2018

Keywords

• nonn

Crossrefs

Cf. A182878.

Programs

Maple

A298567 := proc(n)
    option remember;
    if n < 7 then
        op(n+1,[1, 0, 1, 1, 1, 4,2]) ;
    else
        -2*(n-1)*procname(n-2)-(2*n-3)*procname(n-3)+(n-2)*procname(n-4)
            -(2*n-5)*procname(n-5)+(n-3)*procname(n-6) ;
        -%/n ;
    end if;
end proc: # R. J. Mathar, Jan 21 2020

Maxima

a(n):=sum(binomial(n-k,2*k-n)^2,k,0,2*n/3);

Formula

G.f.: 1/sqrt((1-x^2)^2+x^6-2*x^5-2*x^3).

D-finite with recurrence: n*a(n) -2*(n-1)*a(n-2)-(2*n-3)*a(n-3)+(n-2)*a(n-4) -(2*n-5)*a(n-5) +(n-3)*a(n-6) = 0. - R. J. Mathar, Jan 21 2020