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 A357721 #10 Feb 16 2025 08:34:04
%S A357721 1,0,-2,9,-28,0,1200,-16464,167904,-1393200,7429240,43124400,
%T A357721 -2404571904,55590286752,-1027511503200,16489054310400,
%U A357721 -222885864448000,1994839594780032,14489184835474272,-1470395490046560000,54581408106475622400,-1608207353670788640000
%N A357721 a(n) = Sum_{k=0..floor(n/2)} (-n)^k * Stirling1(n,2*k).
%H A357721 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PochhammerSymbol.html">Pochhammer Symbol</a>.
%F A357721 a(n) = n! * [x^n] cos( sqrt(n) * log(1+x) ).
%F A357721 a(n) = (-1)^n * ( (sqrt(n) * i)_n + (-sqrt(n) * i)_n )/2, where (x)_n is the Pochhammer symbol and i is the imaginary unit.
%o A357721 (PARI) a(n) = sum(k=0, n\2, (-n)^k*stirling(n, 2*k, 1));
%o A357721 (PARI) a(n) = round(n!*polcoef(cos(sqrt(n)*log(1+x+x*O(x^n))), n));
%o A357721 (PARI) a(n) = (-1)^n*round((prod(k=0, n-1, sqrt(n)*I+k)+prod(k=0, n-1, -sqrt(n)*I+k)))/2;
%Y A357721 Main diagonal of A357720.
%Y A357721 Cf. A357683, A357729.
%K A357721 sign
%O A357721 0,3
%A A357721 _Seiichi Manyama_, Oct 10 2022