A368367 - OEIS

%I #26 Jan 31 2024 13:09:33

%S 0,1,405,1112193,83733135993,442674314320893489,

%T 252729042985343953175786217,20874524971928676951126081870191637441,

%U 321062452616441231930929630956482460885924054669273,1152310647749051621143585533734466768135769634034830754169423308849

%N AGM transform of factorials.

%C See A368366 for further information.

%H Paolo Xausa, <a href="/A368367/b368367.txt">Table of n, a(n) for n = 1..30</a>

%t A368367[n_] := With[{f = Range[n]!}, Total[f]^n - n^n*Apply[Times, f]];

%t Array[A368367, 10] (* _Paolo Xausa_, Jan 29 2024 *)

%o (Python)

%o from math import prod, factorial

%o def A368367(n): return sum(factorial(i) for i in range(1,n+1))**n-n**n*prod(i**(n-i+1) for i in range(2,n+1)) # _Chai Wah Wu_, Jan 25 2024

%Y Cf. A000142, A368366.

%K nonn

%O 1,3

%A _N. J. A. Sloane_, Jan 24 2024