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 A352252 #19 Feb 17 2025 08:18:03
%S A352252 1,1,2,3,0,-55,-480,-3157,-15232,-16623,898560,16316179,194574336,
%T A352252 1666248025,5418649600,-170157839685,-5164467978240,-92955464490463,
%U A352252 -1188910801354752,-7329026447550685,157257042777866240,7516793832172469481,187200588993188069376
%N A352252 Expansion of e.g.f. 1 / (1 - x * cos(x)).
%H A352252 Seiichi Manyama, <a href="/A352252/b352252.txt">Table of n, a(n) for n = 0..456</a>
%F A352252 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * binomial(n,2*k+1) * (2*k+1) * a(n-2*k-1).
%F A352252 a(n) = Sum_{k=0..n} k! * i^(n-k) * A185951(n,k), where i is the imaginary unit. - _Seiichi Manyama_, Feb 17 2025
%t A352252 nmax = 22; CoefficientList[Series[1/(1 - x Cos[x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A352252 a[0] = 1; a[n_] := a[n] = Sum[(-1)^k Binomial[n, 2 k + 1] (2 k + 1) a[n - 2 k - 1], {k, 0, Floor[(n - 1)/2]}]; Table[a[n], {n, 0, 22}]
%o A352252 (PARI) my(x='x+O('x^30)); Vec(serlaplace(1 / (1 - x * cos(x)))) \\ _Michel Marcus_, Mar 10 2022
%o A352252 (PARI) a185951(n, k) = binomial(n, k)/2^k*sum(j=0, k, (2*j-k)^(n-k)*binomial(k, j));
%o A352252 a(n) = sum(k=0, n, k!*I^(n-k)*a185951(n, k)); \\ _Seiichi Manyama_, Feb 17 2025
%Y A352252 Cf. A000111, A007289, A009189, A094088, A205571, A302397, A352250, A352251.
%K A352252 sign
%O A352252 0,3
%A A352252 _Ilya Gutkovskiy_, Mar 09 2022