A258789 - OEIS

%I #9 Jun 11 2015 06:25:35

%S 1,1,5,27,169,1115,7760,55748,411498,3101490,23785645,185064559,

%T 1457664666,11602828475,93205739436,754751603157,6155229065861,

%U 50515624923790,416930705579538,3458726257239312,28825340825747729,241245120218823892,2026803168946440648

%N a(n) = [x^n] Product_{k=1..n} 1/(x^(2*k)*(1-x^k)).

%H Vaclav Kotesovec, <a href="/A258789/b258789.txt">Table of n, a(n) for n = 0..380</a>

%F a(n) ~ c * d^n / n^2, where d = A258268 = 9.15337019245412246194853029240135454007332720412184884968926320147613... = r^3/(r-1), where r is the root of the equation polylog(2, 1-r) + 3*log(r)^2/2 = 0, c = 0.8069142856822510276258439534144172057548... .

%p T:=proc(n, k) option remember; `if`(n=0 or k=1, 1, T(n, k-1) + `if`(n<k, 0, T(n-k, k))) end proc: seq(T(n*(n+2), n), n=0..30);

%t Table[SeriesCoefficient[1/Product[x^(2*k)*(1-x^k), {k, 1, n}], {x, 0, n}], {n, 0, 30}]

%t Table[SeriesCoefficient[1/Product[1-x^k, {k, 1, n}], {x, 0, n*(n+2)}], {n, 0, 30}]

%Y Cf. A258268, A258788, A258791, A258793, A258794.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Jun 10 2015