A376489 G.f. satisfies A(x) = 1 / (1 - x^2*A(x)^2 / (1 - x)).

1, 0, 1, 1, 4, 7, 22, 49, 143, 359, 1025, 2742, 7812, 21666, 62044, 175927, 507484, 1460297, 4243802, 12340559, 36108354, 105839241, 311551092, 919000678, 2719362502, 8063263402, 23967845874, 71379427920, 213010634136, 636757780808, 1906765570820

Offset

0,5

Links

Table of n, a(n) for n=0..30.

Formula

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

D-finite with recurrence 8*n*(n+1)*a(n) -28*n*(n-1)*a(n-1) +2*(-9*n^2-n+14)*a(n-2) +(115*n^2-463*n+426)*a(n-3) +4*(-26*n^2+168*n-265)*a(n-4) +3*(3*n-13)*(3*n-14)*a(n-5)=0. - R. J. Mathar, Sep 26 2024

Maple

A376489 := proc(n)
    add(binomial(3*k, k)*binomial(n-k-1, n-2*k)/(2*k+1), k=0..floor(n/2)) ;
end proc:
seq(A376489(n), n=0..70) ; # R. J. Mathar, Sep 26 2024

Prog

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

Crossrefs

Cf. A002212, A376490, A376491.

Sequence in context: A026548 A100098 A127361 * A128533 A162559 A126094

Adjacent sequences: A376486 A376487 A376488 * A376490 A376491 A376492

Keyword

nonn

Author

Seiichi Manyama, Sep 25 2024

Status

approved