A361739 Diagonal of rational function 1/(1 - (x^3 + y^3 + z^3 + x^4*y*z)).

1, 0, 0, 6, 6, 0, 90, 180, 90, 1680, 5040, 5040, 36330, 138600, 207900, 895356, 3818430, 7567560, 24720696, 106702596, 258053796, 742135680, 3050807760, 8483450976, 23450218506, 89691647760, 273414861720, 760735601340, 2713845780360, 8733512193120, 24957399366900

Offset

0,4

Links

Winston de Greef, Table of n, a(n) for n = 0..1935

Formula

a(n) = Sum_{k=0..floor(n/3)} (3*k)!/k!^3 * binomial(k,n-3*k).

From Vaclav Kotesovec, Mar 23 2023: (Start)

Recurrence: (n-1)*n^2*a(n) = -(n-1)^2*n*a(n-1) + 27*(n-2)*(n-1)^2*a(n-3) + 18*(n-2)*(3*n^2 - 9*n + 2)*a(n-4) + 3*n*(3*n - 11)*(3*n - 7)*a(n-5).

a(n) ~ sqrt(3) * d^n / (2*Pi*n), where d = 3.278393896770041178744966998018587... is the positive real root of the equation d^4 - 27*d - 27 = 0. (End)

Prog

(PARI) a(n) = sum(k=0, n\3, (3*k)!/k!^3*binomial(k, n-3*k));

Crossrefs

Cf. A361737, A361738.

Cf. A361730.

Sequence in context: A021942 A346536 A317577 * A245173 A256273 A046620

Adjacent sequences: A361736 A361737 A361738 * A361740 A361741 A361742

Keyword

nonn

Author

Seiichi Manyama, Mar 22 2023

Status

approved