%I #15 May 22 2024 11:33:26

%S 1,0,0,1,1,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,6,6,7,7,8,8,9,10,11,12,14,15,

%T 17,19,21,23,26,28,31,34,37,40,44,47,51,55,59,63,69,73,79,85,92,98,

%U 107,114,124,133,144,154,168,179,194,208,225,240,260,277,299,319,343,365,393,417,447,476

%N Number of partitions of n such that (smallest part) >= 3*(number of parts).

%F G.f.: Sum_{k>=0} x^(3*k^2)/Product_{j=1..k} (1-x^j).

%o (PARI) my(N=80, x='x+O('x^N)); Vec(sum(k=0, N, x^(3*k^2)/prod(j=1, k, 1-x^j)))

%Y Cf. A003114, A373067, A373069, A373070.

%Y Cf. A350894, A373074.

%K nonn

%O 0,13

%A _Seiichi Manyama_, May 22 2024