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Number of partitions of n such that (smallest part) >= 5*(number of parts).
4

%I #14 May 22 2024 11:33:37

%S 1,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,

%T 9,9,10,10,11,11,12,12,13,13,14,15,16,17,19,20,22,24,26,28,31,33,36,

%U 39,42,45,49,52,56,60,64,68,73,77,82,87,92,97,103,108,114,120,126,132,139,145,153,160,168,176,186,194

%N Number of partitions of n such that (smallest part) >= 5*(number of parts).

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

%o (PARI) my(N=90, x='x+O('x^N)); Vec(sum(k=0, N, x^(5*k^2)/prod(j=1, k, 1-x^j)))

%Y Cf. A003114, A373067, A373068, A373069.

%Y Cf. A350899, A373076.

%K nonn

%O 0,21

%A _Seiichi Manyama_, May 22 2024