login
Number of partitions of n into distinct parts such that number of parts is a multiples of 5.
2

%I #20 May 23 2024 11:56:58

%S 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,2,3,5,7,10,13,18,23,30,37,47,57,70,

%T 84,101,119,141,164,192,221,255,291,333,377,427,480,540,603,674,748,

%U 831,918,1014,1115,1226,1342,1469,1602,1748,1899,2064,2236,2423,2618,2829,3049,3288,3537,3807

%N Number of partitions of n into distinct parts such that number of parts is a multiples of 5.

%F G.f.: Sum_{k>=0} x^(5*k*(5*k+1)/2) / Product_{j=1..5*k} (1-x^j) = Sum_{k>=0} Product_{j=1..5*k} (x^j/(1-x^j)).

%o (PARI) my(N=70, x='x+O('x^N)); Vec(sum(k=0, N, prod(j=1, 5*k, x^j/(1-x^j))))

%Y Cf. A000009, A067661, A370747, A372703.

%Y Cf. A363047.

%K nonn

%O 0,18

%A _Seiichi Manyama_, May 23 2024