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%I #6 Dec 01 2015 10:22:21
%S 1,1,4,108,67500,1134472500,2009787236572500,343390991123754492187500,
%T 18843880602308850038793150000000000,
%U 370904101895245095313565571450000000000000000000,6335115544513765517772271190776403515352524800000000000000000000
%N a(n) = Product_{k=0..n} p(k)^k, where p(k) is the partition function A000041.
%F a(n) ~ c * Product_{k=1..n} ( (exp(Pi*sqrt(2/3*(k-1/24))) / (4*sqrt(3)*(k-1/24)) * (1 - sqrt(3/(2*(k-1/24)))/Pi)) )^k, where c = A259405 = 0.90866166764445489256...
%t Table[Product[PartitionsP[k]^k,{k,0,n}],{n,0,10}]
%Y Cf. A000041, A058694, A133018, A259314, A259405, A265097.
%K nonn
%O 0,3
%A _Vaclav Kotesovec_, Jun 25 2015
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