%I #8 May 22 2024 11:33:33

%S 1,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,9,

%T 10,10,11,11,12,13,14,15,17,18,20,22,24,26,29,31,34,37,40,43,47,50,54,

%U 58,62,66,71,75,80,85,90,95,101,106,113,119,126,133,142,149,159,168,179,189,202

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

%C This sequence is different from A350894.

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

%o (PARI) my(N=80, x='x+O('x^N)); Vec(sum(k=0, N, x^(4*k^2+k)/prod(j=1, k, 1-x^j)))

%Y Cf. A003106, A373073, A373074, A373076.

%Y Cf. A350898, A373069.

%K nonn

%O 0,19

%A _Seiichi Manyama_, May 22 2024