A259373 a(n) = Product_{k=0..n} p(k)^k, where p(k) is the partition function A000041.

1, 1, 4, 108, 67500, 1134472500, 2009787236572500, 343390991123754492187500, 18843880602308850038793150000000000, 370904101895245095313565571450000000000000000000, 6335115544513765517772271190776403515352524800000000000000000000

Offset: 0

Author

Vaclav Kotesovec, Jun 25 2015

Keywords

• nonn

Crossrefs

Cf. A000041, A058694, A133018, A259314, A259405, A265097.

Programs

Mathematica

Table[Product[PartitionsP[k]^k,{k,0,n}],{n,0,10}]

Formula

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...