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 A335644 #15 Oct 04 2020 07:01:33
%S A335644 1,1,1,3,1,-23,-2,-28,-2435,253,118966,158400,-5277106,-6453094,
%T A335644 377003877,150562341,-38919169331,-49489639843,4097920244054,
%U A335644 15989402021656,-397866849121614,-3949517739363706,34992745696351023,937723673130987379,-2417716098650478930,-223227071403982903362
%N A335644 Expansion of e.g.f. Product_{k>0} (1 + sin(x)^k / k!).
%F A335644 E.g.f.: exp( Sum_{i>0} Sum_{j>0} (-1)^(i+1)*sin(x)^(i*j)/(i*(j!)^i) ).
%t A335644 max = 25; Range[0, max]! * CoefficientList[Series[Product[1 + Sin[x]^k/k!, {k, 1, max}], {x, 0, max}], x] (* _Amiram Eldar_, Oct 04 2020 *)
%o A335644 (PARI) N=40; x='x+O('x^N); Vec(serlaplace(prod(k=1, N, 1+sin(x)^k/k!)))
%o A335644 (PARI) N=40; x='x+O('x^N); Vec(serlaplace(exp(sum(i=1, N, sum(j=1, N\i, (-1)^(i+1)*sin(x)^(i*j)/(i*j!^i))))))
%Y A335644 Cf. A007837, A335629, A335637, A335642, A336046.
%K A335644 sign
%O A335644 0,4
%A A335644 _Seiichi Manyama_, Oct 03 2020