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%I #22 May 14 2023 23:47:41
%S 0,0,0,0,0,1,1,2,3,5,7,11,13,19,24,32,39,52,61,77,93,114,133,164,188,
%T 226,261,309,353,417,471,549,622,717,808,933,1042,1191,1334,1516,1690,
%U 1921,2131,2407,2674,3006,3330,3744,4135,4628,5116,5708,6294,7020
%N Number of partitions of n such that 5*(least part) = greatest part.
%H David A. Corneth, <a href="/A237827/b237827.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Alois P. Heinz)
%F G.f.: Sum_{k>=1} x^(6*k)/Product_{j=k..5*k} (1-x^j). - _Seiichi Manyama_, May 14 2023
%e a(8) = 2 counts these partitions: 521, 5111.
%t z = 64; q[n_] := q[n] = IntegerPartitions[n];
%t Table[Count[q[n], p_ /; 3 Min[p] = = Max[p]], {n, z}] (* A237825*)
%t Table[Count[q[n], p_ /; 4 Min[p] = = Max[p]], {n, z}] (* A237826 *)
%t Table[Count[q[n], p_ /; 5 Min[p] = = Max[p]], {n, z}] (* A237827 *)
%t Table[Count[q[n], p_ /; 2 Min[p] + 1 = = Max[p]], {n, z}] (* A237828 *)
%t Table[Count[q[n], p_ /; 2 Min[p] - 1 = = Max[p]], {n, z}] (* A237829 *)
%o (PARI) my(N=60, x='x+O('x^N)); concat([0, 0, 0, 0, 0], Vec(sum(k=1, N, x^(6*k)/prod(j=k, 5*k, 1-x^j)))) \\ _Seiichi Manyama_, May 14 2023
%Y Cf. A000041, A117086, A237757, A237828, A237829.
%Y Cf. A118096, A237825, A237826.
%K nonn,easy
%O 1,8
%A _Clark Kimberling_, Feb 16 2014
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