A382240 a(n) = Sum_{k=0..n} 3^((n+k-1)*(n-k)/2) * n! / (n-k)!.

1, 2, 11, 168, 7233, 889014, 314965899, 323989244676, 972969439627809, 8566667168429128842, 221877626825222187484203, 16949442370817602102051560384, 3827091229259231090623800852526113, 2558686452439976557585601153755243553406, 5072634396431144733070212976874036427346208619

Offset: 0

Author

Vaclav Kotesovec, Mar 19 2025

Keywords

• nonn

Comments

In general, for m>1, Sum_{k=0..n} m^((n+k-1)*(n-k)/2) * n! / (n-k)! ~ sqrt(2*Pi/log(m)) * n^(log(n)/(2*log(m)) + 1/2) * m^((2*n - 1)^2/8).

Crossrefs

Cf. A379614.

Programs

Mathematica

Table[Sum[3^((n+k-1)*(n-k)/2) * n!/(n-k)!, {k, 0, n}], {n, 0, 15}]

Formula

a(n) ~ sqrt(2*Pi/log(3)) * n^(log(n)/(2*log(3)) + 1/2) * 3^((2*n-1)^2/8).