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 A329259 #4 Nov 09 2019 16:28:48
%S A329259 0,1,1,2,7,29,150,930,6755,56071,523540,5430710,61967070,771361525,
%T A329259 10402051660,151065164250,2350567168951,39013029955917,
%U A329259 687979755287416,12845920452293594,253183788618567525,5252704310496986070,114424576082127987830,2611313756103949479660
%N A329259 Expansion of e.g.f. -log(1 - Sum_{k>=1} x^(k^2) / (k^2)!).
%F A329259 a(0) = 0; a(n) = A010052(n) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * A010052(n-k) * k * a(k).
%t A329259 nmax = 23; CoefficientList[Series[-Log[1 - Sum[x^(k^2)/(k^2)!, {k, 1, Floor[nmax^(1/2)] + 1}]], {x, 0, nmax}], x] Range[0, nmax]!
%t A329259 a[n_] := a[n] = Boole[IntegerQ[n^(1/2)]] + Sum[Binomial[n, k] Boole[IntegerQ[(n - k)^(1/2)]] k a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 23}]
%Y A329259 Cf. A000629, A010052, A205803, A205804, A329256, A329258.
%K A329259 nonn
%O A329259 0,4
%A A329259 _Ilya Gutkovskiy_, Nov 09 2019