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 A330019 #4 Nov 27 2019 12:53:01
%S A330019 1,1,4,21,150,1330,14180,176295,2505230,40049226,711379872,
%T A330019 13899553206,296270826852,6841305568812,170127212242416,
%U A330019 4532854743105975,128824523061126750,3890041395675793930,124375112406132404960,4197530354920789582410,149118181703716510545260
%N A330019 Expansion of e.g.f. 1 / (1 - Sum_{k>=1} binomial(k,floor(k/2)) * x^k / k!).
%F A330019 E.g.f.: 1 / (2 - BesselI(0,2*x) - BesselI(1,2*x)).
%F A330019 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n,k) * A001405(k) * a(n-k).
%t A330019 nmax = 20; CoefficientList[Series[1/(2 - BesselI[0, 2 x] - BesselI[1, 2 x]), {x, 0, nmax}], x] Range[0, nmax]!
%t A330019 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n, k] Binomial[k, Floor[k/2]] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 20}]
%Y A330019 Cf. A001405, A054341, A305561, A308849, A328004.
%K A330019 nonn
%O A330019 0,3
%A A330019 _Ilya Gutkovskiy_, Nov 27 2019