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 A363214 #16 Feb 24 2024 13:41:20
%S A363214 0,0,0,0,0,1,0,1,1,2,2,4,4,7,7,11,13,19,21,30,35,47,55,73,85,111,131,
%T A363214 166,197,247,291,362,428,525,620,756,890,1078,1268,1523,1791,2140,
%U A363214 2507,2983,3490,4131,4824,5688,6626,7785,9052,10595,12298,14351,16618,19339,22355,25938
%N A363214 Number of partitions of n with rank 5 (the rank of a partition is the largest part minus the number of parts).
%H A363214 Seiichi Manyama, <a href="/A363214/b363214.txt">Table of n, a(n) for n = 1..10000</a>
%F A363214 G.f.: (1/Product_{k>=1} (1-x^k)) * Sum_{k>=1} (-1)^(k-1) * x^(5*k) * ( x^(k*(3*k-1)/2) - x^(k*(3*k+1)/2) ).
%t A363214 Table[Count[IntegerPartitions[n],_?(#[[1]]-Length[#]==5&)],{n,60}] (* _Harvey P. Dale_, Feb 24 2024 *)
%o A363214 (PARI) my(N=60, x='x+O('x^N)); concat([0, 0, 0, 0, 0], Vec(1/prod(k=1, N, 1-x^k)*sum(k=1, N, (-1)^(k-1)*x^(5*k)*(x^(k*(3*k-1)/2)-x^(k*(3*k+1)/2)))))
%Y A363214 Column k=5 in the triangle A063995.
%Y A363214 Column r=5 of A105806.
%Y A363214 Cf. A000041.
%K A363214 nonn
%O A363214 1,10
%A A363214 _Seiichi Manyama_, May 21 2023