A300974 a(n) = [x^n] Product_{k>=1} 1/(1 - x^(k^2))^n.
1, 1, 3, 10, 39, 151, 588, 2304, 9111, 36307, 145553, 586246, 2370264, 9614242, 39105580, 159444160, 651468967, 2666771488, 10934393619, 44899828056, 184616878289, 760010818689, 3132147583744, 12921037206764, 53351800567200, 220478125956426, 911839751015196, 3773836780169050
Offset: 0
Keywords
Links
Programs
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Maple
a:= proc(m) option remember; local b; b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add( binomial(m+j-1, j)*b(n-i^2*j, i-1), j=0..n/i^2))) end: b(n, isqrt(n)) end: seq(a(n), n=0..30); # Alois P. Heinz, Mar 17 2018 -
Mathematica
Table[SeriesCoefficient[Product[1/(1 - x^k^2)^n, {k, 1, n}], {x, 0, n}], {n, 0, 27}]
Formula
From Vaclav Kotesovec, Mar 23 2018: (Start)
a(n) ~ c * d^n / sqrt(n), where
d = 4.216358447600641565890184638418336163396695730036... and
c = 0.26442245016754864773722176155288663999776... (End)
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