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%I #7 Nov 14 2018 14:01:51
%S 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 550,618,883,1024,1395,1810,2372,2985,3682,4762,6077,7634,10160,12517,
%U 15448,19820,24754,32108,40085,50851,62331,78548,98505,125596,156565
%N Expansion of Product_{k>=1} 1/(1 - x^prime(k))^A056768(k).
%C a(n) is the number of partitions of n into prime parts prime(k) of A056768(k) kinds.
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F G.f.: Product_{k>=1} 1/(1 - x^A000040(k))^A000607(A000040(k)).
%e a(7) = 6 because we have [{7}], [{5, 2}], [{5}, {2}], [{3, 2, 2}], [{3, 2}, {2}] and [{3}, {2}, {2}].
%t 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 Cf. A000040, A000607, A001970, A056768, A300300.
%K nonn
%O 0,6
%A _Ilya Gutkovskiy_, Nov 11 2018
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