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 A337749 #15 Nov 28 2021 13:41:07
%S A337749 1,1,-1,-5,13,101,-389,-4241,21785,305353,-1960649,-33588829,
%T A337749 258805669,5239857325,-47102631757,-1100370038249,11304631621681,
%U A337749 299300650403729,-3459217276234385,-102360822438075317,1314502564969066301,42991545423991633141,-607300185015708631061
%N A337749 a(n) = n! * Sum_{k=0..floor(n/2)} (-1)^k / (n-2*k)!.
%H A337749 Seiichi Manyama, <a href="/A337749/b337749.txt">Table of n, a(n) for n = 0..449</a>
%F A337749 G.f.: Sum_{k>=0} (-1)^k * (2*k)! * x^(2*k) / (1 - x)^(2*k+1).
%F A337749 E.g.f.: exp(x) / (1 + x^2).
%F A337749 a(0) = a(1) = 1; a(n) = 1 - n * (n-1) * a(n-2).
%t A337749 Table[n! Sum[(-1)^k/(n - 2 k)!, {k, 0, Floor[n/2]}], {n, 0, 22}]
%t A337749 nmax = 22; CoefficientList[Series[Exp[x]/(1 + x^2), {x, 0, nmax}], x] Range[0, nmax]!
%t A337749 (* alternative code *)
%t A337749 f[x_]:=I*(ExpIntegralE[-x,I]*E^I-ExpIntegralE[-x,-I]*E^(-I))/2
%t A337749 FunctionExpand[Array[f,20,0]] (* _Velin Yanev_, Oct 13 2021 *)
%o A337749 (PARI) a(n) = n!*sum(k=0, n\2, (-1)^k / (n-2*k)!); \\ _Michel Marcus_, Sep 18 2020
%Y A337749 Cf. A087208, A182386, A337750, A337751.
%K A337749 sign
%O A337749 0,4
%A A337749 _Ilya Gutkovskiy_, Sep 18 2020