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Expansion of Product_{k>=1} 1/(1 - x^prime(k))^2.
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%I #14 Jan 12 2021 10:11:11

%S 1,0,2,2,3,6,7,12,15,22,30,40,54,72,93,122,157,202,256,326,409,512,

%T 640,792,981,1204,1479,1802,2196,2662,3218,3880,4660,5588,6677,7960,

%U 9471,11232,13299,15710,18514,21784,25570,29968,35047,40922,47698,55500,64480,74786,86618

%N Expansion of Product_{k>=1} 1/(1 - x^prime(k))^2.

%C Number of partitions of n into prime parts of 2 kinds.

%C Self-convolution of A000607.

%H Vaclav Kotesovec, <a href="/A298436/b298436.txt">Table of n, a(n) for n = 0..10000</a> (terms 0..1000 from Seiichi Manyama)

%H <a href="/index/Par#part">Index entries for related partition-counting sequences</a>

%F G.f.: Product_{k>=1} 1/(1 - x^prime(k))^2.

%F log(a(n)) ~ 2*Pi*sqrt(2*n/(3*log(n/2))). - _Vaclav Kotesovec_, Jan 12 2021

%e a(5) = 6 because we have [5a], [5b], [3a, 2a], [3a, 2b], [3b, 2a] and [3b, 2b].

%t nmax = 50; CoefficientList[Series[Product[1/(1 - x^Prime[k])^2, {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000040, A000607, A000712, A280245.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jan 19 2018