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 A352253 #12 Mar 10 2022 08:27:03
%S A352253 1,1,8,153,5492,316625,26774622,3121729709,479962730648,
%T A352253 94087054172673,22904161764512570,6778870099212235805,
%U A352253 2397161662661680925364,998186321121004312238513,483430830256916593106991782,269435322393253822641626419725,171224984800186115316322226731952
%N A352253 Expansion of e.g.f. 1 / (1 - x * sinh(x) / 2) (even powers only).
%F A352253 a(0) = 1; a(n) = Sum_{k=1..n} binomial(2*n,2*k) * k * a(n-k).
%t A352253 nmax = 32; Take[CoefficientList[Series[1/(1 - x Sinh[x]/2), {x, 0, nmax}], x] Range[0, nmax]!, {1, -1, 2}]
%t A352253 a[0] = 1; a[n_] := a[n] = Sum[Binomial[2 n, 2 k] k a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 16}]
%o A352253 (PARI) my(x='x+O('x^40), v=Vec(serlaplace(1 /(1-x*sinh(x)/2)))); vector(#v\2, k, v[2*k-1]) \\ _Michel Marcus_, Mar 10 2022
%Y A352253 Cf. A006153, A006154, A094088, A205571, A352251, A352254.
%K A352253 nonn
%O A352253 0,3
%A A352253 _Ilya Gutkovskiy_, Mar 09 2022