A261736 - OEIS

%I #15 Feb 13 2024 11:36:26

%S 1,-1,0,-1,1,-1,2,-2,2,-3,3,-3,5,-5,5,-7,8,-8,11,-12,12,-16,17,-18,23,

%T -25,26,-32,35,-37,45,-49,52,-62,67,-72,85,-92,98,-114,124,-133,153,

%U -166,178,-203,220,-236,268,-290,311,-350,379,-407,456,-493,529

%N Expansion of Product_{k>=1} (1 + x^(6*k))/(1 + x^k).

%H Seiichi Manyama, <a href="/A261736/b261736.txt">Table of n, a(n) for n = 0..10000</a>

%H David J. Hemmer, <a href="https://arxiv.org/abs/2402.03643">Generating functions for fixed points of the Mullineux map</a>, arXiv:2402.03643 [math.CO], 2024.

%H Vaclav Kotesovec, <a href="http://arxiv.org/abs/1509.08708">A method of finding the asymptotics of q-series based on the convolution of generating functions</a>, arXiv:1509.08708 [math.CO], Sep 30 2015, p. 14.

%F a(n) ~ (-1)^n * exp(sqrt(2*n)*Pi/3) / (2^(7/4)*sqrt(3)*n^(3/4)).

%p seq(coeff(series(mul((1+x^(6*k))/(1+x^k),k=1..n), x,n+1),x,n),n=0..60); # _Muniru A Asiru_, Jul 29 2018

%t nmax = 100; CoefficientList[Series[Product[(1 + x^(6*k))/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]

%Y Cf. A081360 (m=2), A109389 (m=3), A261734 (m=4), A133563 (m=5), A113297 (m=7), A261735 (m=8), A261733 (m=9), A145707 (m=10).

%K sign

%O 0,7

%A _Vaclav Kotesovec_, Aug 30 2015