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 A344935 #27 Aug 19 2022 04:31:10
%S A344935 1,2,3,6,25,130,779,5446,43569,392130,3921299,43134278,517611337,
%T A344935 6728947394,94205263515,1413078952710,22609263243361,384357475137154,
%U A344935 6918434552468771,131450256496906630,2629005129938132601,55209107728700784642,1214600370031417262123
%N A344935 a(0)=1; for n > 0, a(n) = n*(a(n-1) + i^(n-1)) if n is odd, n*a(n-1) + i^n otherwise, where i = sqrt(-1).
%F A344935 E.g.f.: (1+x)*cos(x)/(1-x).
%F A344935 Lim_{n->infinity} a(n)/n! = 2*cos(1) = 2*A049470.
%F A344935 D-finite with recurrence a(n) -n*a(n-1) +2*a(n-2) +2*(-n+2)*a(n-3) +a(n-4) +(-n+4)*a(n-5)=0. - _R. J. Mathar_, Aug 19 2022
%e A344935 a(0) = 1;
%e A344935 a(1) = 1*(a(0) + i^(1-1)) = 2;
%e A344935 a(2) = 2*a(1) + i^2 = 3;
%e A344935 a(3) = 3*(a(2) + i^2) = 6;
%e A344935 a(4) = 4*a(3) + i^4 = 25.
%p A344935 A344935 := proc(n)
%p A344935 option remember ;
%p A344935 if n = 0 then
%p A344935 1;
%p A344935 elif type(n,'odd') then
%p A344935 n*(procname(n-1)+I^(n-1)) ;
%p A344935 else
%p A344935 n*procname(n-1)+I^n ;
%p A344935 end if;
%p A344935 simplify(%) ;
%p A344935 end proc:
%p A344935 seq(A344935(n),n=0..40) ; # _R. J. Mathar_, Aug 19 2022
%t A344935 a[0] = 1; a[n_] := a[n] = If[OddQ[n], n*(a[n - 1] + I^(n - 1)), n*a[n - 1] + I^n]; Array[a, 30, 0] (* _Amiram Eldar_, Jun 03 2021 *)
%o A344935 (PARI) a(n) = if (n==0, 1, if (n%2, n*(a(n-1) + I^(n-1)), n*a(n-1) + I^n)); \\ _Michel Marcus_, Jun 05 2021
%Y A344935 Cf. A344262, A344419, A049470, A009001.
%K A344935 nonn
%O A344935 0,2
%A A344935 _Amrit Awasthi_, Jun 03 2021