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 A213424 #11 Jul 05 2025 06:22:28
%S A213424 1,0,1,0,1,1,1,1,2,1,3,2,3,3,5,4,6,6,8,8,12,10,15,15,19,21,26,26,34,
%T A213424 36,45,47,59,61,76,83,97,107,128,137,165,179,210,231,271,296,345,380,
%U A213424 438,485,561,614,708,783,893,991,1129,1246,1420,1572,1781
%N A213424 Number of partitions of n in which all parts are >= 2 and the largest part occurs at least five times.
%F A213424 a(n) = A186445(n) - 2*A186445(n-1) + A186445(n-2).
%F A213424 G.f.: (1-x)*Product_{k>4} 1/(1-x^k).
%F A213424 a(n) ~ Pi^5 * exp(Pi*sqrt(2*n/3))/ (18*sqrt(2)*n^(7/2)). - _Vaclav Kotesovec_, Jul 05 2025
%e A213424 For n = 20 we have three partitions: {[4+4+4+4+4], [3+3+3+3+3+3+2], [2+2+2+2+2+2+2+2+2+2]}, so a(20) = 3.
%t A213424 nmax = 100; Drop[CoefficientList[Series[(1 - x)^2*(1 - x^2)*(1 - x^3)*(1 - x^4) / Product[1 - x^k, {k, 1, nmax}], {x, 0, nmax}], x], 10] (* _Vaclav Kotesovec_, Jul 05 2025 *)
%Y A213424 Cf. A000041, A186445, A213423.
%K A213424 nonn
%O A213424 10,9
%A A213424 _Mircea Merca_, Jun 11 2012