A285243 Expansion of Product_{k>=1} 1/(1 - k*x^(k^2))^k.

1, 1, 1, 1, 5, 5, 5, 5, 17, 26, 26, 26, 58, 94, 94, 94, 190, 298, 352, 352, 608, 896, 1112, 1112, 1752, 2641, 3289, 3559, 5095, 7499, 9227, 10307, 14051, 20111, 25520, 28760, 38843, 53467, 68191, 76831, 102187, 138283, 175543, 202813, 263905, 355220, 445364

Offset: 0

Author

Vaclav Kotesovec, Apr 15 2017

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A285047, A266941, A285241, A285242, A285245.

Programs

Mathematica

nmax = 100; CoefficientList[Series[Product[1/(1 - k*x^(k^2))^k, {k,1,nmax}], {x,0,nmax}], x]

Formula

a(n) ~ c * n * 2^(n/4), where

c = 37.4093119651465404809069752821426852731608123... if mod(n,4)=0

c = 37.6275180026872367633343656570058911570800766... if mod(n,4)=1

c = 37.7650387085085950514850376086515488784106690... if mod(n,4)=2

c = 37.4702467422193571732026074780460498930830447... if mod(n,4)=3