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A277386 a(n) = Sum_{k=0..n} binomial(n, k)^3 * 3^(n-k) * k!. 1
1, 4, 35, 438, 6873, 127488, 2703447, 64121130, 1674999009, 47638235484, 1461975938379, 48068355965886, 1683311251028265, 62477888170824792, 2447583053876363727, 100842325515959413842, 4356021203508275392833, 196739133595421931988020, 9268144156277932321747251 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..18.

FORMULA

Recurrence: n*(8*n - 23)*a(n) = 3*(8*n^3 - 15*n^2 - 30*n + 17)*a(n-1) - (n-1)*(24*n^3 - 261*n^2 + 770*n - 666)*a(n-2) + (n-2)^3*(n-1)*(8*n - 15)*a(n-3).

a(n) ~ n^(n - 1/6) * exp(3*3^(1/3)*n^(2/3) - 3^(2/3)*n^(1/3) - n +1) / (3^(5/6)*sqrt(2*Pi)) * (1 + 19/(6*3^(2/3)*n^(1/3)) + 1193/(1080*3^(1/3) * n^(2/3))).

MATHEMATICA

Table[Sum[Binomial[n, k]^3 * 3^(n-k) * k!, {k, 0, n}], {n, 0, 20}]

CROSSREFS

Cf. A000172, A277382, A241247, A274246.

Sequence in context: A324314 A123224 A160887 * A183878 A132694 A270917

Adjacent sequences:  A277383 A277384 A277385 * A277387 A277388 A277389

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Oct 12 2016

STATUS

approved

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Last modified August 8 19:29 EDT 2020. Contains 336298 sequences. (Running on oeis4.)