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 A321508 #7 Nov 14 2018 14:01:51
%S A321508 1,0,1,1,1,3,2,6,4,7,10,15,17,30,31,41,58,81,105,143,177,218,306,393,
%T A321508 550,618,883,1024,1395,1810,2372,2985,3682,4762,6077,7634,10160,12517,
%U A321508 15448,19820,24754,32108,40085,50851,62331,78548,98505,125596,156565
%N A321508 Expansion of Product_{k>=1} 1/(1 - x^prime(k))^A056768(k).
%C A321508 a(n) is the number of partitions of n into prime parts prime(k) of A056768(k) kinds.
%H A321508 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A321508 G.f.: Product_{k>=1} 1/(1 - x^A000040(k))^A000607(A000040(k)).
%e A321508 a(7) = 6 because we have [{7}], [{5, 2}], [{5}, {2}], [{3, 2, 2}], [{3, 2}, {2}] and [{3}, {2}, {2}].
%t A321508 b[n_] := b[n] = SeriesCoefficient[Product[1/(1 - x^Prime[k]), {k, 1, n}], {x, 0, Prime[n]}]; a[n_] := a[n] = SeriesCoefficient[Product[1/(1 - x^Prime[k])^b[k], {k, 1, n}], {x, 0, n}]; Table[a[n], {n, 0, 48}]
%Y A321508 Cf. A000040, A000607, A001970, A056768, A300300.
%K A321508 nonn
%O A321508 0,6
%A A321508 _Ilya Gutkovskiy_, Nov 11 2018