This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A370747 #61 May 23 2024 11:56:47
%S A370747 1,0,0,0,0,0,1,1,2,3,4,5,7,8,10,12,14,16,19,21,24,28,31,35,40,45,51,
%T A370747 59,66,76,87,100,114,133,151,175,201,232,265,307,349,402,458,524,594,
%U A370747 680,767,872,983,1112,1248,1409,1575,1770,1976,2211,2460,2748,3048,3393,3759,4173,4612,5112
%N A370747 Number of partitions of n into distinct parts such that number of parts is a multiples of 3.
%F A370747 G.f.: Sum_{k>=0} x^(3*k*(3*k+1)/2) / Product_{j=1..3*k} (1-x^j) = Sum_{k>=0} Product_{j=1..3*k} (x^j/(1-x^j)).
%e A370747 a(12) = 7 counts these partitions: 921, 831, 741, 732, 651, 642, 543.
%o A370747 (PARI) my(N=70, x='x+O('x^N)); Vec(sum(k=0, N, prod(j=1, 3*k, x^j/(1-x^j))))
%Y A370747 Cf. A000009, A067661, A372703, A373078.
%Y A370747 Cf. A363045.
%K A370747 nonn
%O A370747 0,9
%A A370747 _Seiichi Manyama_, May 23 2024