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a(n) = Sum_{i=(n*n-n+2)/2..(n*n+n)/2} i!.
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%I #12 Mar 15 2022 13:15:05

%S 1,8,864,4037040,1401598598400,53652268264218624000,

%T 316196664157721349185863680000,

%U 382630662500715988102392981826830336000000,122342346998826334909002798912467017444232685158400000000,12931604174610554670466196146308122246477496321113350463375278080000000000

%N a(n) = Sum_{i=(n*n-n+2)/2..(n*n+n)/2} i!.

%e a(4) = 7! + 8! + 9! + 10! = 4037074.

%o (PARI) a(n)= sum(i=(n^2-n+2)/2, (n^2+n)/2, i!); \\ _Michel Marcus_, Mar 15 2022

%Y Cf. A000142.

%K easy,nonn

%O 1,2

%A _Ctibor O. Zizka_, May 07 2010

%E a(4) corrected and more terms from _Michel Marcus_, Mar 15 2022