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 A346749 #4 Aug 01 2021 16:40:16
%S A346749 1,0,1,2,7,26,124,628,3565,22096,149176,1080868,8372543,68957268,
%T A346749 601351748,5528967282,53416626441,540682811424,5718911631856,
%U A346749 63060992662328,723382253378395,8616075340134868,106374847828850676,1359171823319541070,17946987240664242493
%N A346749 E.g.f.: exp( (x * (1 + x) * exp(x) - sinh(x)) / 4 ).
%C A346749 Exponential transform of A002620.
%F A346749 a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002620(k) * a(n-k).
%t A346749 nmax = 24; CoefficientList[Series[Exp[(x (1 + x) Exp[x] - Sinh[x])/4], {x, 0, nmax}], x] Range[0, nmax]!
%t A346749 a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] Floor[k^2/4] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]
%Y A346749 Cf. A002620, A003724, A033462.
%K A346749 nonn
%O A346749 0,4
%A A346749 _Ilya Gutkovskiy_, Aug 01 2021