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A343928 a(n) = Sum_{k=0..n} (k!)^n * binomial(n,k).

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%I A343928 #16 May 05 2021 01:54:17
%S A343928 1,2,7,244,337061,24923091206,139331988275478727,
%T A343928 82607113404338664216300296,6984967577834038055008791270166057993,
%U A343928 109110690950275218023122492287310115968068596613130,395940866518366059877297056617763923418318903997411043997258716171
%N A343928 a(n) = Sum_{k=0..n} (k!)^n * binomial(n,k).
%H A343928 Seiichi Manyama, <a href="/A343928/b343928.txt">Table of n, a(n) for n = 0..30</a>
%F A343928 a(n) = [x^n] Sum_{k>=0} (k!)^n * x^k/(1 - x)^(k+1).
%F A343928 a(n) = n! * [x^n] exp(x) * Sum_{k>=0} (k!)^(n-1) * x^k.
%t A343928 a[n_] := Sum[(k!)^n * Binomial[n, k], {k, 0, n} ]; Array[a, 11, 0] (* _Amiram Eldar_, May 04 2021 *)
%o A343928 (PARI) a(n) = sum(k=0, n, k!^n*binomial(n, k));
%Y A343928 Cf. A000522, A046662, A072034, A336247, A339311, A343898, A343899, A343929.
%K A343928 nonn
%O A343928 0,2
%A A343928 _Seiichi Manyama_, May 04 2021