A364161 G.f. satisfies A(x) = 1 + x*A(x)^2/(1 - x^3*A(x)).

1, 1, 2, 5, 15, 47, 153, 514, 1769, 6205, 22102, 79733, 290721, 1069688, 3966739, 14810348, 55627778, 210046102, 796864028, 3035912900, 11610468138, 44556451207, 171529074168, 662238211929, 2563524741603, 9947573055828, 38687704042595

Offset

0,3

Links

Table of n, a(n) for n=0..26.

Formula

a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,k) * binomial(2*n-5*k+1,n-3*k)/(2*n-5*k+1).

D-finite with recurrence (n+1)*a(n) +2*(-2*n+1)*a(n-1) +(n+1)*a(n-2) +3*(-2*n+3)*a(n-3) +(-2*n+7)*a(n-5) +(n-8)*a(n-6) +(n-8)*a(n-8)=0. - R. J. Mathar, Aug 29 2023

Maple

A364161 := proc(n)
    add( binomial(n-2*k-1, k)*binomial(2*n-5*k+1, n-3*k)/(2*n5*k+1), k=0..floor(n/3)) ;
end proc:
seq(A364161(n), n=0..80); # R. J. Mathar, Aug 29 2023

Prog

(PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, k)*binomial(2*n-5*k+1, n-3*k)/(2*n-5*k+1));

Crossrefs

Cf. A001003, A119370.

Cf. A218251, A364833, A365247.

Sequence in context: A148363 A365267 A350434 * A148364 A172405 A149915

Adjacent sequences: A364158 A364159 A364160 * A364162 A364163 A364164

Keyword

nonn

Author

Seiichi Manyama, Aug 28 2023

Status

approved