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 A347987 #20 May 27 2025 03:43:36
%S A347987 1,1,11,-75,3969,-140595,7374191,-435638203,30421321073,
%T A347987 -2409092861175,214562251828275,-21195275581114635,
%U A347987 2301157855016159905,-272330254968023391035,34894294917147760652775,-4812715265513253499593675,710922905477027337578759265,-111981455662673544130741177455
%N A347987 a(n) = [x^n] (2*n)! * Sum_{k=0..2*n} binomial(x,k).
%H A347987 Seiichi Manyama, <a href="/A347987/b347987.txt">Table of n, a(n) for n = 0..326</a>
%F A347987 a(n) = A054651(2*n,n) = A190782(2*n,n).
%F A347987 a(n) = [x^(2*n)] ((2*n)!/n!) * (log(1 + x))^n/(1 - x).
%F A347987 a(n) ~ (-1)^n * c * d^n * (n-1)!, where d = 8*w^2/(2*w-1), where w = -LambertW(-1,-exp(-1/2)/2) = 1.7564312086261696769827376166... and c = 0.07543488970038444052522917317552747476381171100725972392415521577... - _Vaclav Kotesovec_, Sep 27 2021, updated May 27 2025
%t A347987 Table[(2*n)!/n! * SeriesCoefficient[Log[1+x]^n/(1-x), {x, 0, 2*n}], {n, 0, 20}] (* _Vaclav Kotesovec_, May 25 2025 *)
%o A347987 (PARI) a(n) = (2*n)!*polcoef(sum(k=n, 2*n, binomial(x, k)), n);
%Y A347987 Cf. A054651, A098118, A190782, A347989.
%K A347987 sign
%O A347987 0,3
%A A347987 _Seiichi Manyama_, Sep 23 2021