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Number of partitions p of n such that (1/4)*max(p) is a part of p.
4

%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