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 A357683 #18 Feb 16 2025 08:34:04
%S A357683 1,0,2,9,60,500,4920,55566,706720,9979200,154706760,2609691700,
%T A357683 47547916416,929943488448,19421810408000,431196538865400,
%U A357683 10137091700736000,251485260368396288,6563768030597826720,179746132716715050000,5152012082327932518400
%N A357683 a(n) = Sum_{k=0..floor(n/2)} n^k * |Stirling1(n,2*k)|.
%H A357683 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PochhammerSymbol.html">Pochhammer Symbol</a>.
%F A357683 a(n) = n! * [x^n] cosh( sqrt(n) * log(1-x) ).
%F A357683 a(n) = ( (sqrt(n))_n + (-sqrt(n))_n )/2, where (x)_n is the Pochhammer symbol.
%F A357683 a(n) ~ n^(n + sqrt(n)/2 - 1/4) / (2*exp(n - sqrt(n) - 1/2)) * (1 - 3/(4*sqrt(n))). - _Vaclav Kotesovec_, Oct 10 2022
%o A357683 (PARI) a(n) = sum(k=0, n\2, n^k*abs(stirling(n, 2*k, 1)));
%o A357683 (PARI) a(n) = round(n!*polcoef(cosh(sqrt(n)*log(1-x+x*O(x^n))), n));
%o A357683 (PARI) a(n) = round((prod(k=0, n-1, sqrt(n)+k)+prod(k=0, n-1, -sqrt(n)+k)))/2;
%Y A357683 Cf. A105752, A263687.
%K A357683 nonn
%O A357683 0,3
%A A357683 _Seiichi Manyama_, Oct 09 2022