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A280366 G.f.: Product_{k>=1} (1 + x^(k*(k+1)/2)) / (1 - x^(k*(k+1)/2)). 8

%I

%S 1,2,2,4,6,6,10,14,14,20,28,30,38,50,54,66,86,94,110,138,152,178,218,

%T 238,274,330,362,412,488,534,602,710,778,864,1006,1102,1220,1410,1542,

%U 1696,1940,2122,2328,2638,2878,3148,3550,3870,4214,4722,5136,5580,6230

%N G.f.: Product_{k>=1} (1 + x^(k*(k+1)/2)) / (1 - x^(k*(k+1)/2)).

%C Convolution of A024940 and A007294.

%H Vaclav Kotesovec, <a href="/A280366/b280366.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) ~ exp(3 * 2^(-4/3) * Pi^(1/3) * ((2*sqrt(2)-1) * Zeta(3/2))^(2/3) * n^(1/3)) * Zeta(3/2) * (2*sqrt(2)-1) / (32 * sqrt(3) * Pi * n^(3/2)).

%t nmax = 60; CoefficientList[Series[Product[(1+x^(k*(k+1)/2))/(1-x^(k*(k+1)/2)), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A024940, A007294, A103265.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Jan 02 2017

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Last modified May 7 02:20 EDT 2021. Contains 343636 sequences. (Running on oeis4.)