Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #15 May 17 2023 08:34:38
%S 1,0,0,0,0,1,1,2,3,5,7,10,13,18,23,31,39,51,64,81,102,128,159,198,245,
%T 304,374,460,563,689,841,1023,1242,1505,1819,2195,2642,3173,3804,4551,
%U 5435,6477,7707,9151,10850,12843,15175,17902,21089,24802,29132,34164,40012,46796,54663,63766
%N Number of partitions p of n such that (1/4)*max(p) is a part of p.
%H Seiichi Manyama, <a href="/A363067/b363067.txt">Table of n, a(n) for n = 0..1000</a>
%F G.f.: Sum_{k>=0} x^(5*k)/Product_{j=1..4*k} (1-x^j).
%e a(8) = 3 counts these partitions: 431, 4211, 41111.
%o (PARI) a(n) = sum(k=0, n\5, #partitions(n-5*k, 4*k));
%Y Cf. A002865, A238479, A363066, A363068.
%Y Cf. A237826, A363046.
%K nonn
%O 0,8
%A _Seiichi Manyama_, May 16 2023