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A361737
Diagonal of rational function 1/(1 - (x + y + z + x^2*y*z)).
2
1, 6, 96, 1860, 39780, 900396, 21146496, 509697936, 12523921740, 312324904320, 7881117611796, 200784546041976, 5156135919980136, 133299228503087640, 3465901878247744920, 90563401722349627920, 2376642701449937741580, 62607393746503658100360
OFFSET
0,2
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. A361728.
Sequence in context: A227262 A001805 A139743 * A156460 A038094 A346184
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 22 2023
STATUS
approved