A375565 a(n) = Sum_{k=0..floor(n/3)} (n-2*k+1) * binomial(n-2*k,k)^2.

1, 2, 3, 6, 17, 42, 90, 194, 441, 1006, 2242, 4950, 10974, 24376, 53961, 119048, 262337, 577782, 1271117, 2792718, 6129342, 13441616, 29454517, 64492800, 141108878, 308542280, 674238780, 1472532300, 3214268735, 7012637490, 15292425923, 33333338466, 72627184389

Offset

0,2

Links

Table of n, a(n) for n=0..32.

Formula

G.f.: (1-x-x^3)/((1-x-x^3)^2 - 4*x^4)^(3/2).

D-finite with recurrence 3*n*(n-1)*a(n) -(8*n-3)*(n-1)*a(n-1) +(7*n^2-14*n+8)*a(n-2) +(-8*n^2+3*n+23)*a(n-3) -2*n*(n+8)*a(n-4) +4*((n-1)^2)*a(n-5) +3*n*(n+2)*a(n-6) -2*n*(n-1)*a(n-7)=0. - R. J. Mathar, Oct 17 2024

Maple

A375565 := proc(n)
    add((n-2*k+1)*binomial(n-2*k, k)^2, k=0..floor(n/3)) ;
end proc:
seq(A375565(n), n=0..80) ; # R. J. Mathar, Oct 17 2024

Prog

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

Crossrefs

Cf. A182884, A376735.

Cf. A246840.

Sequence in context: A018284 A204514 A338594 * A078344 A024498 A319283

Adjacent sequences: A375562 A375563 A375564 * A375566 A375567 A375568

Keyword

nonn

Author

Seiichi Manyama, Oct 17 2024

Status

approved