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A266819 Expansion of Product_{k>=1} ((1 + x^k) * (1 + 2*x^k)). 3

%I #9 Jan 04 2016 08:51:47

%S 1,3,5,12,20,33,60,93,144,222,340,498,729,1050,1486,2115,2946,4068,

%T 5592,7608,10278,13854,18483,24528,32426,42594,55677,72498,94008,

%U 121290,156002,199842,255012,324438,411318,519771,655128,823056,1031148,1288590,1605945

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

%C Convolution of A000009 and A032302.

%H Vaclav Kotesovec, <a href="/A266819/b266819.txt">Table of n, a(n) for n = 0..5000</a>

%F a(n) ~ c^(1/4) * exp(2*sqrt(c*n)) / (2*sqrt(6*Pi)*n^(3/4)), where c = Pi^2/4 + log(2)^2/2 + polylog(2, -1/2) = 2.259213400307794164599109607216595948859... .

%t nmax = 50; CoefficientList[Series[Product[(1+x^k) * (1+2*x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A000009, A032302, A266820, A266822.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jan 04 2016

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Last modified April 14 18:28 EDT 2024. Contains 371667 sequences. (Running on oeis4.)