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A306241 a(n) = Sum_{k=0..n} (k*n)!/n!^k.

%I A306241 #17 May 19 2024 20:44:22
%S A306241 1,2,8,1702,63097722,623372476627154,2670179107513625597282318,
%T A306241 7363615751879726008424500256018442794,
%U A306241 18165723935734974232438957032838329596079311234990642
%N A306241 a(n) = Sum_{k=0..n} (k*n)!/n!^k.
%H A306241 Seiichi Manyama, <a href="/A306241/b306241.txt">Table of n, a(n) for n = 0..26</a>
%F A306241 a(n) equals (row sums of A120666) + 1.
%F A306241 From _Vaclav Kotesovec_, Feb 08 2019: (Start)
%F A306241 a(n) ~ A034841(n).
%F A306241 a(n) ~ n^(n^2 - n/2 + 1) / (exp(1/12) * (2*Pi)^((n-1)/2)). (End)
%t A306241 Table[Sum[(k*n)!/n!^k,{k,0,n}],{n,0,10}] (* _Vaclav Kotesovec_, Feb 08 2019 *)
%o A306241 (PARI) {a(n) = sum(k=0, n, (k*n)!/n!^k)}
%Y A306241 Cf. A034841, A120666, A221177.
%K A306241 nonn
%O A306241 0,2
%A A306241 _Seiichi Manyama_, Jan 31 2019