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%I #15 Jan 24 2022 08:29:58
%S 0,0,1,0,0,0,1,1,1,1,2,2,2,2,4,4,6,7,10,10,13,14,19,21,27,31,40,45,55,
%T 64,79,91,111,127,154,177,211,243,290,333,394,455,538,618,726,834,977,
%U 1121,1304,1495,1738,1989,2302,2633,3041,3473,3999,4562,5241
%N Number of partitions of n such that 3*(greatest part) = (number of parts).
%C Also, the number of partitions of n such that (greatest part) = 3*(number of parts).
%H Seiichi Manyama, <a href="/A237756/b237756.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: Sum_{k>=1} x^(4*k-1) * Product_{j=1..k-1} (1-x^(3*k+j-1)/(1-x^j). - _Seiichi Manyama_, Jan 24 2022
%e a(15) = 4 counts these partitions: [12,1,1,1], [9,5,1], [9,4,2], [9,3,3].
%t z = 50; Table[Count[IntegerPartitions[n], p_ /; Max[p] = = 3 Length[p]], {n, z}]
%o (PARI) my(N=66, x='x+O('x^N)); concat([0, 0], Vec(sum(k=1, N, x^(4*k-1)*prod(j=1, k-1, (1-x^(3*k+j-1))/(1-x^j))))) \\ _Seiichi Manyama_, Jan 24 2022
%Y Column 3 of A350879.
%Y Cf. A064173, A237753, A350892, A350894.
%K nonn,easy
%O 1,11
%A _Clark Kimberling_, Feb 13 2014
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