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 A363213 #14 May 22 2023 08:10:16
%S A363213 0,0,0,0,1,0,1,1,2,2,4,4,6,7,11,12,18,20,28,33,44,51,68,80,103,122,
%T A363213 154,182,229,270,334,396,485,572,698,822,993,1169,1404,1649,1971,2310,
%U A363213 2745,3214,3803,4439,5235,6099,7162,8331,9750,11315,13205,15294,17794,20574,23872
%N A363213 Number of partitions of n with rank 4 (the rank of a partition is the largest part minus the number of parts).
%H A363213 Seiichi Manyama, <a href="/A363213/b363213.txt">Table of n, a(n) for n = 1..10000</a>
%F A363213 G.f.: (1/Product_{k>=1} (1-x^k)) * Sum_{k>=1} (-1)^(k-1) * x^(4*k) * ( x^(k*(3*k-1)/2) - x^(k*(3*k+1)/2) ).
%o A363213 (PARI) my(N=60, x='x+O('x^N)); concat([0, 0, 0, 0], Vec(1/prod(k=1, N, 1-x^k)*sum(k=1, N, (-1)^(k-1)*x^(4*k)*(x^(k*(3*k-1)/2)-x^(k*(3*k+1)/2)))))
%Y A363213 Column k=4 in the triangle A063995.
%Y A363213 Column r=4 of A105806.
%Y A363213 Cf. A000041.
%K A363213 nonn
%O A363213 1,9
%A A363213 _Seiichi Manyama_, May 21 2023