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 A344099 #5 May 09 2021 11:17:00
%S A344099 1,1,5,20,60,190,561,1651,4720,13300,36716,99872,267836,708890,
%T A344099 1854255,4796273,12279445,31135188,78236006,194921680,481758832,
%U A344099 1181675902,2877646681,6959866116,16723591530,39934902812,94795718409,223741936855,525206126933,1226393510220
%N A344099 Expansion of Product_{k>=1} (1 + x^k)^binomial(k+3,4).
%F A344099 G.f.: exp( Sum_{k>=1} (-1)^(k+1) * x^k / (k*(1 - x^k)^5) ).
%t A344099 nmax = 29; CoefficientList[Series[Product[(1 + x^k)^Binomial[k + 3, 4], {k, 1, nmax}], {x, 0, nmax}], x]
%t A344099 a[n_] := a[n] = If[n == 0, 1, (1/n) Sum[Sum[(-1)^(k/d + 1) d Binomial[d + 3, 4], {d, Divisors[k]}] a[n - k], {k, 1, n}]]; Table[a[n], {n, 0, 29}]
%Y A344099 Cf. A000332, A000391, A028377, A258343, A305206, A344100, A344101.
%K A344099 nonn
%O A344099 0,3
%A A344099 _Ilya Gutkovskiy_, May 09 2021