A364437 G.f. satisfies A(x) = 1 - x*(1 - 2*A(x)^3).

1, 1, 6, 42, 326, 2712, 23676, 214068, 1987488, 18838464, 181548960, 1773566208, 17523740592, 174814263088, 1758342057504, 17812729393248, 181581358338528, 1861259423846400, 19172185074938112, 198354225907274496, 2060279149742042112

Offset

0,3

Links

Table of n, a(n) for n=0..20.

Formula

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

D-finite with recurrence n*(2*n+1)*a(n) +3*(-11*n^2+14*n-4)*a(n-1) +27*(5*n-7) *(n-2)*a(n-2) -27*(7*n-16)*(n-3)*a(n-3) +81*(n-3)*(n-4)*a(n-4)=0. - R. J. Mathar, Jul 25 2023

Maple

A364437 := proc(n)
    (-1)^n*add((-2)^k* binomial(n, k) * binomial(3*k+1, n) / (3*k+1), k=0..n) ;
end proc:
seq(A364437(n), n=0..70); # R. J. Mathar, Jul 25 2023

Prog

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

Crossrefs

Cf. A068764.

Sequence in context: A142985 A118351 A033296 * A218755 A165314 A082302

Adjacent sequences: A364434 A364435 A364436 * A364438 A364439 A364440

Keyword

nonn

Author

Seiichi Manyama, Jul 24 2023

Status

approved