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 A355268 #15 Feb 28 2024 09:08:11
%S A355268 1,1,4,12,60,300,1920,13440,109200,982800,9858240,108440640,
%T A355268 1301952960,16925388480,236972736000,3554591040000,56873975558400,
%U A355268 966857584492800,17403454164096000,330665629117824000,6613313252799052800,138879578308780108800,3055350750951750451200
%N A355268 a(n) = n! * [x^n] -exp(x^2)/(x - 1).
%H A355268 Seiichi Manyama, <a href="/A355268/b355268.txt">Table of n, a(n) for n = 0..449</a>
%F A355268 a(n) = n!*hypergeom([-floor(n/2)], [-floor(n/2)], 1).
%F A355268 a(n) = n!*Sum_{k=0..floor(n/2)} 1/k!. - _Seiichi Manyama_, Jul 17 2022
%F A355268 D-finite with recurrence a(n) -n*a(n-1) +2*(-n+1)*a(n-2) +2*(n-1)*(n-2)*a(n-3)=0. - _R. J. Mathar_, Jul 27 2022
%F A355268 a(n) ~ exp(1) * n!. - _Vaclav Kotesovec_, Feb 28 2024
%p A355268 egf := -exp(x^2)/(x - 1): ser := series(egf, x, 26):
%p A355268 seq(n!*coeff(ser, x, n), n = 0..22);
%o A355268 (PARI) a(n) = n!*sum(k=0, n\2, 1/k!); \\ _Seiichi Manyama_, Jul 17 2022
%Y A355268 Cf. A000522.
%K A355268 nonn
%O A355268 0,3
%A A355268 _Peter Luschny_, Jul 15 2022