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.
%I A295610 #11 Feb 16 2025 08:33:52
%S A295610 1,2,7,256,345749,25090776406,139507578065088907,
%T A295610 82622801516492599819822772,6985137485409222182920705065038896201,
%U A295610 109110989095384931538566720095053550173384985449034,395940975233113726268241745444050219538058574725338743701918216111
%N A295610 a(n) = Sum_{k=0..n} (n!/(n - k)!)^k.
%H A295610 Seiichi Manyama, <a href="/A295610/b295610.txt">Table of n, a(n) for n = 0..30</a>
%H A295610 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BinomialSums.html">Binomial Sums</a>
%F A295610 a(n) = Sum_{k=0..n} A219206(n,k)*A036740(k).
%F A295610 a(n) ~ 2^(n/2) * Pi^(n/2) * n^(n^2 + n/2) / exp(n^2 - 1/12). - _Vaclav Kotesovec_, Nov 25 2017
%t A295610 Table[Sum[(n!/(n - k)!)^k, {k, 0, n}], {n, 0, 10}]
%t A295610 Table[Sum[(Gamma[n + 1]/Gamma[k + 1])^(n - k), {k, 0, n}], {n, 0, 10}]
%t A295610 Table[Sum[(Binomial[n, k] k!)^k, {k, 0, n}], {n, 0, 10}]
%o A295610 (PARI) a(n) = sum(k=0, n, (n!/(n - k)!)^k); \\ _Michel Marcus_, Nov 25 2017
%Y A295610 Cf. A000522, A006040, A036740, A217284, A219206.
%K A295610 nonn
%O A295610 0,2
%A A295610 _Ilya Gutkovskiy_, Nov 24 2017