This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A382240 #6 Mar 20 2025 10:16:47
%S A382240 1,2,11,168,7233,889014,314965899,323989244676,972969439627809,
%T A382240 8566667168429128842,221877626825222187484203,
%U A382240 16949442370817602102051560384,3827091229259231090623800852526113,2558686452439976557585601153755243553406,5072634396431144733070212976874036427346208619
%N A382240 a(n) = Sum_{k=0..n} 3^((n+k-1)*(n-k)/2) * n! / (n-k)!.
%C A382240 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).
%F A382240 a(n) ~ sqrt(2*Pi/log(3)) * n^(log(n)/(2*log(3)) + 1/2) * 3^((2*n-1)^2/8).
%t A382240 Table[Sum[3^((n+k-1)*(n-k)/2) * n!/(n-k)!, {k, 0, n}], {n, 0, 15}]
%Y A382240 Cf. A379614.
%K A382240 nonn
%O A382240 0,2
%A A382240 _Vaclav Kotesovec_, Mar 19 2025