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a(n) = Sum_{k=1..n} (k!)^n.
3

%I #16 Apr 28 2021 02:04:15

%S 1,5,225,333089,24891170433,139317055679149697,

%T 82606511560391889386751489,6984964663477899063759529684476994049,

%U 109110688697205077023425816926479750793809817618433,395940866162019279867473563258123776010342586429441374123441432577

%N a(n) = Sum_{k=1..n} (k!)^n.

%H Seiichi Manyama, <a href="/A339311/b339311.txt">Table of n, a(n) for n = 1..30</a>

%t a[n_] := Sum[(k!)^n, {k, 1, n}]; Array[a, 10] (* _Amiram Eldar_, Apr 28 2021 *)

%o (PARI) {a(n) = sum(k=1, n, k!^n)}

%Y Sum_{k=1..n} (k!)^m: A007489 (m=1), A104344 (m=2), A138564 (m=3), A289945 (m=4), A316777 (m=5), A289946 (m=6).

%Y Cf. A000142, A112999.

%K nonn

%O 1,2

%A _Seiichi Manyama_, Nov 29 2020