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Number of partitions of n into distinct parts such that number of parts is a multiples of 4.
2

%I #34 May 23 2024 11:56:51

%S 1,0,0,0,0,0,0,0,0,0,1,1,2,3,5,6,9,11,15,18,23,27,34,39,47,54,64,72,

%T 84,94,108,120,136,150,169,185,207,226,251,273,302,328,362,393,433,

%U 470,518,563,621,677,748,818,906,994,1104,1216,1354,1497,1671,1853,2073,2305,2582,2877,3226,3599

%N Number of partitions of n into distinct parts such that number of parts is a multiples of 4.

%F G.f.: Sum_{k>=0} x^(2*k*(4*k+1)) / Product_{j=1..4*k} (1-x^j) = Sum_{k>=0} Product_{j=1..4*k} (x^j/(1-x^j)).

%o (PARI) my(N=70, x='x+O('x^N)); Vec(sum(k=0, N, prod(j=1, 4*k, x^j/(1-x^j))))

%Y Cf. A000009, A067661, A370747, A373078.

%Y Cf. A363046.

%K nonn

%O 0,13

%A _Seiichi Manyama_, May 23 2024