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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.

A374653 a(n) = Sum_{k=1..n+1} (k + 1)(n - k + 1)!.

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%I A374653 #8 Jul 28 2024 17:06:08
%S A374653 5,11,27,85,359,1953,12907,99461,871455,8538169,92409683,1094367597,
%T A374653 14071365511,195177925025,2904454929339,46151637341653,
%U A374653 779850886057967,13962610118134281,264033196462146595,5258262698750606909,110001474536281307223
%N A374653 a(n) = Sum_{k=1..n+1} (k + 1)(n - k + 1)!.
%t A374653 t[n_] := Sum[ (k + 1)*(n - k + 1)!, {k, 1, n + 1}]
%t A374653 Table[t[n], {n, 1, 30}]
%Y A374653 Cf. A374652.
%K A374653 nonn
%O A374653 1,1
%A A374653 _Clark Kimberling_, Jul 25 2024