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 A350893 #17 Jan 24 2022 04:41:42
%S A350893 0,1,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,10,10,
%T A350893 12,13,15,16,19,20,23,25,28,30,34,36,40,43,47,50,56,59,65,70,77,82,91,
%U A350893 97,107,115,126,135,149,159,174,187,204,218,238,254,276,295,320,341,370,394,426,455,491,523,565
%N A350893 Number of partitions of n such that (smallest part) = 2*(number of parts).
%F A350893 G.f.: Sum_{k>=1} x^(2*k^2)/Product_{j=1..k-1} (1-x^j).
%F A350893 a(n) ~ (1 - alfa) * exp(2*sqrt(n*(2*log(alfa)^2 + polylog(2, 1 - alfa)))) * (2*log(alfa)^2 + polylog(2, 1 - alfa))^(1/4) / (2*sqrt(Pi) * sqrt(4 - 3*alfa) * n^(3/4)), where alfa = 0.72449195900051561158837228218703656578649448135... is positive real root of the equation alfa^4 + alfa - 1 = 0. - _Vaclav Kotesovec_, Jan 21 2022
%t A350893 nmax = 100; Rest[CoefficientList[1 + Series[Sum[x^(2*j^2)*(1 - x^j)/Product[1 - x^i, {i, 1, j}], {j, 1, nmax}], {x, 0, nmax}], x]] (* _Vaclav Kotesovec_, Jan 21 2022 *)
%o A350893 (PARI) my(N=99, x='x+O('x^N)); concat(0, Vec(sum(k=1, sqrtint(N\2), x^(2*k^2)/prod(j=1, k-1, 1-x^j))))
%Y A350893 Column 2 of A350890.
%Y A350893 Cf. A168656, A237753, A237757.
%K A350893 nonn
%O A350893 1,18
%A A350893 _Seiichi Manyama_, Jan 21 2022