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 A039899 #25 Jan 14 2022 11:34:33
%S A039899 0,0,1,2,3,5,8,12,18,25,36,49,68,91,123,162,214,278,362,464,596,757,
%T A039899 961,1209,1521,1897,2366,2931,3627,4463,5487,6711,8200,9976,12121,
%U A039899 14672,17738,21371,25716,30852,36964,44168,52709,62746,74600,88497
%N A039899 Number of partitions satisfying 0 < cn(0,5) + cn(2,5) + cn(3,5).
%C A039899 For a given partition cn(i,n) means the number of its parts equal to i modulo n.
%C A039899 Short: o < 0 + 2 + 3 (OMZBBp).
%C A039899 Number of partitions of n such that (greatest part) > (multiplicity of greatest part), for n >= 1. For example, a(6) counts these 8 partitions: 6, 51, 42, 411, 33, 321, 3111, 21111. See the Mathematica program at A240057 for the sequence as a count of partitions defined in this manner, and related sequences. - _Clark Kimberling_, Apr 02 2014
%H A039899 Alois P. Heinz, <a href="/A039899/b039899.txt">Table of n, a(n) for n = 0..1000</a>
%F A039899 G.f.: Sum_{k>=0} x^k * (1-x^(k*(k-1))) / Product_{j=1..k} (1-x^j). - _Seiichi Manyama_, Jan 13 2022
%p A039899 b:= proc(n, i, t) option remember; `if`(n=0, t,
%p A039899 `if`(i<1, 0, b(n, i-1, t)+ `if`(i>n, 0, b(n-i, i,
%p A039899 `if`(irem(i, 5) in {1, 4}, t, 1)))))
%p A039899 end:
%p A039899 a:= n-> b(n$2, 0):
%p A039899 seq(a(n), n=0..50); # _Alois P. Heinz_, Apr 03 2014
%t A039899 Table[Count[IntegerPartitions[n], p_ /; Min[p] < Length[p]], {n, 24}] (* _Clark Kimberling_, Feb 13 2014 *)
%t A039899 b[n_, i_, t_] := b[n, i, t] = If[n==0, t, If[i<1, 0, b[n, i-1, t] + If[i > n, 0, b[n-i, i, If[MemberQ[{1, 4}, Mod[i, 5]], t, 1]]]]]; a[n_] := b[n, n, 0]; Table[a[n], {n, 0, 50}] (* _Jean-François Alcover_, Nov 16 2015, after _Alois P. Heinz_ *)
%o A039899 (PARI) my(N=66, x='x+O('x^N)); concat([0, 0], Vec(sum(k=0, N, x^k*(1-x^(k*(k-1)))/prod(j=1, k, 1-x^j)))) \\ _Seiichi Manyama_, Jan 13 2022
%Y A039899 Cf. A003106, A003114, A039900, A237976.
%K A039899 nonn
%O A039899 0,4
%A A039899 _Olivier Gérard_