A361737 Diagonal of rational function 1/(1 - (x + y + z + x^2*y*z)).

1, 6, 96, 1860, 39780, 900396, 21146496, 509697936, 12523921740, 312324904320, 7881117611796, 200784546041976, 5156135919980136, 133299228503087640, 3465901878247744920, 90563401722349627920, 2376642701449937741580, 62607393746503658100360

Offset

0,2

Links

Table of n, a(n) for n=0..17.

Formula

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

a(n) ~ sqrt(3) * ((27 + 3*sqrt(93))/2)^n / (2*Pi*n). - Vaclav Kotesovec, Mar 23 2023

Mathematica

Table[Sum[(3*k)!/k!^3 * Binomial[k, n-k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 23 2023 *)

Prog

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

Crossrefs

Cf. A361738, A361739.

Cf. A361728.

Sequence in context: A227262 A001805 A139743 * A156460 A038094 A346184

Adjacent sequences: A361734 A361735 A361736 * A361738 A361739 A361740

Keyword

nonn

Author

Seiichi Manyama, Mar 22 2023

Status

approved