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A266138 Expansion of Product_{k>=1} 1/(1 - k*(x^(2*k+1))). 2

%I #5 Dec 21 2015 16:19:42

%S 1,0,0,1,0,2,1,3,2,5,7,7,11,13,24,26,35,44,69,78,112,150,188,245,318,

%T 429,537,729,924,1177,1534,1965,2518,3287,4108,5394,6857,8604,11022,

%U 14073,17899,22549,28900,36182,45954,58395,72912,92118,116201,146279

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

%H Vaclav Kotesovec, <a href="/A266138/b266138.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ c * 3^(n/7), where

%F c = 617630.638335... if mod(n,7) = 0

%F c = 617630.321433... if mod(n,7) = 1

%F c = 617630.360795... if mod(n,7) = 2

%F c = 617630.429073... if mod(n,7) = 3

%F c = 617630.357078... if mod(n,7) = 4

%F c = 617630.421636... if mod(n,7) = 5

%F c = 617630.341606... if mod(n,7) = 6.

%t nmax=80; CoefficientList[Series[Product[1/(1-k*(x^(2*k+1))), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A006906, A077335, A087897, A265951, A266137.

%K nonn

%O 0,6

%A _Vaclav Kotesovec_, Dec 21 2015

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