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 A367256 #15 Jan 31 2024 08:07:10
%S A367256 1,1,5,46,593,9726,192637,4457580,117769409,3492894070,114790042901,
%T A367256 4137157889316,162154385331985,6863637142316332,311905306734621069,
%U A367256 15140756439172826776,781693659313991730945,42759819036520142319270,2469943332976774829606821
%N A367256 a(n) = Sum_{k=0..n} binomial(n, k) * binomial(n - 1, k - 1) * n^(n - k).
%H A367256 Paolo Xausa, <a href="/A367256/b367256.txt">Table of n, a(n) for n = 0..350</a>
%F A367256 a(n) = Sum_{k=0..n} A367267(n, k) * n^(n - k).
%F A367256 a(n) = n*n^(n - 1)*hypergeom([1 - n, 1 - n], [2], 1/n) for n > 0.
%F A367256 a(n) ~ exp(2*sqrt(n) - 1) * n^(n - 3/4) / (2*sqrt(Pi)). - _Vaclav Kotesovec_, Nov 11 2023
%p A367256 a := n -> if n= 0 then 1 else n*n^(n - 1)*hypergeom([1 - n, 1 - n], [2], 1/n) fi:
%p A367256 seq(simplify(a(n)), n = 0..19);
%t A367256 A367256[n_] := If[n == 0, 1, n*n^(n-1)*Hypergeometric2F1[1-n, 1-n, 2, 1/n]];
%t A367256 Array[A367256, 25, 0] (* _Paolo Xausa_, Jan 31 2024 *)
%Y A367256 Cf. A187021, A367267, A367257.
%K A367256 nonn
%O A367256 0,3
%A A367256 _Peter Luschny_, Nov 11 2023