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 A349103 #22 Mar 28 2022 07:42:58
%S A349103 1,1,1,-1,-7,-16,19,270,809,-1832,-26939,-81680,415817,5085192,
%T A349103 11943199,-154023064,-1510744111,-1192784896,80798373289,615743987520,
%U A349103 -1348945040647,-55570193758592,-296824726927253,2567750854163200,47111874571146041
%N A349103 Expansion of e.g.f. exp( (sin(x) + x*cos(x))/2 ).
%H A349103 Seiichi Manyama, <a href="/A349103/b349103.txt">Table of n, a(n) for n = 0..571</a>
%F A349103 a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/2)} (-1)^k * (k+1) * binomial(n-1,2*k) * a(n-2*k-1).
%t A349103 With[{m = 24}, Range[0, m]! * CoefficientList[Series[Exp[(Sin[x] + x*Cos[x])/2], {x, 0, m}], x]] (* _Amiram Eldar_, Mar 26 2022 *)
%o A349103 (PARI) my(N=40, x='x+O('x^N)); Vec(serlaplace(exp((sin(x)+x*cos(x))/2)))
%o A349103 (PARI) a(n) = if(n==0, 1, sum(k=0, (n-1)\2, (-1)^k*(k+1)*binomial(n-1, 2*k)*a(n-2*k-1)));
%Y A349103 Cf. A002017, A009189, A349104, A351937.
%K A349103 sign
%O A349103 0,5
%A A349103 _Seiichi Manyama_, Mar 26 2022