|
%I #14 Jan 24 2022 08:31:20
%S 0,1,0,0,1,1,1,2,1,2,3,4,5,7,7,9,12,15,17,23,27,34,42,50,60,75,87,106,
%T 128,154,182,222,260,311,369,437,515,613,716,845,993,1166,1361,1599,
%U 1861,2176,2534,2950,3422,3983,4605,5339,6174,7136,8227,9500,10928
%N Number of partitions of n such that 2*(greatest part) = (number of parts).
%C Also, the number of partitions of n such that (greatest part) = 2*(number of parts); hence, the number of partitions of n such that (rank + greatest part) = 0.
%H Seiichi Manyama, <a href="/A237753/b237753.txt">Table of n, a(n) for n = 1..1000</a>
%F G.f.: Sum_{k>=1} x^(3*k-1) * Product_{j=1..k-1} (1-x^(2*k+j-1)/(1-x^j). - _Seiichi Manyama_, Jan 24 2022
%e a(8) = 2 counts these partitions: 311111, 2222.
%t z = 50; Table[Count[IntegerPartitions[n], p_ /; 2 Max[p] = = Length[p]], {n, z}]
%o (PARI) my(N=66, x='x+O('x^N)); concat(0, Vec(sum(k=1, N, x^(3*k-1)*prod(j=1, k-1, (1-x^(2*k+j-1))/(1-x^j))))) \\ _Seiichi Manyama_, Jan 24 2022
%Y Column 2 of A350879.
%Y Cf. A064173, A237751, A237752, A237754-A237757, A350893.
%K nonn,easy
%O 1,8
%A _Clark Kimberling_, Feb 13 2014
|
