A372019 G.f. A(x) satisfies A(x) = ( 1 + 9*x*A(x)/(1 - x*A(x)) )^(1/3).

1, 3, 3, 3, 30, 57, 84, 867, 1893, 3162, 33132, 76953, 136812, 1446204, 3478764, 6420387, 68260134, 167946159, 317782524, 3392340186, 8479140510, 16332164868, 174873206424, 442212416121, 863222622780, 9264327739716, 23637757714788, 46624054987452

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

a(n) = (1/(n+1)) * Sum_{k=0..n} 9^k * binomial(n/3+1/3,k) * binomial(n-1,n-k).

D-finite with recurrence n*(n-1)*(n+1)*a(n) -8*(2*n-5)*(8*n^2-40*n+57)*a(n-3) +4096*(n-5)*(n-6)*(n-4)*a(n-6)=0. - R. J. Mathar, Apr 22 2024

Maple

A371019 := proc(n)
    add(9^k*binomial((n+1)/3, k)*binomial(n-1, k-1), k=0..n) ;
    %/(n+1) ;
end proc:
seq(A371019(n), n=0..60) ; # R. J. Mathar, Apr 22 2024

Prog

(PARI) a(n) = sum(k=0, n, 9^k*binomial(n/3+1/3, k)*binomial(n-1, n-k))/(n+1);

Crossrefs

Cf. A372018, A372020.

Cf. A372004.

Sequence in context: A033874 A122092 A230495 * A369081 A346909 A369232

Adjacent sequences: A372016 A372017 A372018 * A372020 A372021 A372022

Keyword

nonn

Author

Seiichi Manyama, Apr 15 2024

Status

approved