A383916 a(n) = Sum_{k=0..n} binomial(2*n, k) * (n-k)^(3*n).

1, 1, 68, 22770, 21143488, 41904629550, 151957171590144, 910666718387157732, 8390164064875701321728, 112583179357513548960803670, 2109812207969377622615440752640, 53397692462483465346961668429307836, 1775866125092261344436828225211633500160, 75857512919848315654302238627976991244564300

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Formula

a(n) ~ 2^(2*n + 1/2) * r^(3*n + 1) * n^(3*n) / (sqrt(3 - r^2) * exp(3*n) * (1 - r^2)^n), where r = 0.92488761106894648930384927930334708844525256369797556858640... is the root of the equation (1 + r)/(1 - r) = exp(3/r).

Mathematica

Join[{1}, Table[Sum[Binomial[2*n, n-k]*k^(3*n), {k, 0, n}], {n, 1, 15}]]

Crossrefs

Cf. A032443, A345876, A209289/2, A383853, A383917.

Sequence in context: A159365 A145623 A307137 * A230685 A093234 A177666

Adjacent sequences: A383913 A383914 A383915 * A383917 A383918 A383919

Keyword

nonn

Author

Vaclav Kotesovec, May 15 2025

Status

approved