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 A383704 #14 May 07 2025 14:57:15
%S A383704 1,2,-34,-540,26614,805980,-66399124,-2972817848,343902030758,
%T A383704 20389669252524,-3039312653124540,-224361715353976200,
%U A383704 40941662601331486396,3617518823154571788440,-781104190733806836937320,-80375840650247250199417200,20044038897159722534821833990
%N A383704 a(n) = [x^n] Product_{k=0..2*n-1} (x - (-1)^k * (2*k+1)).
%H A383704 Vincenzo Librandi, <a href="/A383704/b383704.txt">Table of n, a(n) for n = 0..200</a>
%F A383704 a(n) = Sum_{k=0..n} (-(4*n-3))^k * 4^(n-k) * binomial(n+k,n) * |Stirling1(2*n,n+k)|.
%F A383704 a(n) = Sum_{k=0..n} (4*n-1)^k * 4^(n-k) * binomial(n+k,n) * Stirling1(2*n,n+k).
%F A383704 a(n) = (2*n)! * [x^(2*n)] 1/f(x)^(4*n-3) * log(f(x))^n / n!, where f(x) = 1/(1 - 4*x)^(1/4).
%t A383704 Table[Sum[(4*n-1)^k*4^(n-k)*Binomial[n+k,n]*StirlingS1[2*n,n+k],{k,0,n}],{n,0,17}] (* _Vincenzo Librandi_, May 07 2025 *)
%o A383704 (PARI) a(n) = polcoef(prod(k=0, 2*n-1, x-(-1)^k*(2*k+1)), n);
%o A383704 (Magma) [&+[((4*n-1)^k * 4^(n-k) * Binomial(n+k,n) * StirlingFirst(2*n,n+k)): k in [0..n]]: n in [0..25]]; // _Vincenzo Librandi_, May 07 2025
%Y A383704 Cf. A293318.
%K A383704 sign
%O A383704 0,2
%A A383704 _Seiichi Manyama_, May 06 2025