|
%I #11 Jul 04 2018 03:16:44
%S 1,2,3,4,5,7,9,12,15,18,22,27,33,40,48,57,67,79,93,109,127,147,170,
%T 196,226,260,298,340,387,440,500,567,641,723,814,916,1030,1156,1295,
%U 1448,1617,1804,2011,2239,2489,2763,3064,3395,3759,4158,4594,5070,5590,6159,6781,7460,8199,9003
%N Expansion of (1/(1 - x))* Product_{k>=1} (1 + x^k)/(1 + x^(3*k)).
%C Partial sums of A003105.
%H Vaclav Kotesovec, <a href="/A304632/b304632.txt">Table of n, a(n) for n = 0..2000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SchursPartitionTheorem.html">Schur's Partition Theorem</a>
%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F G.f.: (1/(1 - x))*Product_{k>=0} 1/((1 - x^(6*k+1))*(1 - x^(6*k+5))).
%F G.f.: (1/(1 - x))*Product_{k>=0} 1/(1 - x^k + x^(2*k)).
%F a(n) ~ exp(sqrt(2*n)*Pi/3) * sqrt(3) / (Pi * 2^(3/4) * n^(1/4)). - _Vaclav Kotesovec_, May 19 2018
%t nmax = 57; CoefficientList[Series[1/(1 - x) Product[(1 + x^k)/(1 + x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x]
%t nmax = 57; CoefficientList[Series[1/(1 - x) Product[1/((1 - x^(6 k + 1)) (1 - x^(6 k + 5))), {k, 0, nmax}], {x, 0, nmax}], x]
%t nmax = 57; CoefficientList[Series[1/(1 - x) Product[1/(1 - x^k + x^(2 k)), {k, 0, nmax}], {x, 0, nmax}], x]
%Y Cf. A000070, A003105, A036469, A304630, A304631.
%K nonn
%O 0,2
%A _Ilya Gutkovskiy_, May 15 2018
|
