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%I A026801 #25 Sep 08 2022 08:44:49
%S A026801 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,2,2,3,3,4,4,5,5,7,7,9,
%T A026801 10,12,13,16,17,21,23,27,30,36,39,46,51,60,66,77,85,99,110,126,140,
%U A026801 162,179,205,228,260,289,329,365,415,461,521,579,655,726,818,909,1022,1134,1273,1411
%N A026801 Number of partitions of n in which the least part is 8.
%H A026801 G. C. Greubel, Table of n, a(n) for n = 1..1000
%H A026801 Jason Kimberley, Index of sequences counting not necessarily connected k-regular simple graphs with girth exactly g
%F A026801 G.f.: x^8 * Product_{m>=8} 1/(1-x^m).
%F A026801 a(n+8) = p(n) -p(n-1) -p(n-2) +p(n-5) +p(n-7) +p(n-8) -p(n-10) -p(n-11) -2*p(n-12) +2*p(n-16) +p(n-17) +p(n-18) -p(n-20) -p(n-21) -p(n-23) +p(n-26) +p(n-27) -p(n-28) where p(n)=A000041(n). - _Shanzhen Gao_, Oct 28 2010
%F A026801 a(n) ~ exp(Pi*sqrt(2*n/3)) * 35*Pi^7 / (18*sqrt(2)*n^(9/2)). - _Vaclav Kotesovec_, Jun 02 2018
%F A026801 G.f.: Sum_{k>=1} x^(8*k) / Product_{j=1..k-1} (1 - x^j). - _Ilya Gutkovskiy_, Nov 25 2020
%p A026801 seq(coeff(series(x^8/mul(1-x^(m+8), m = 0..80), x, n+1), x, n), n = 1..70); # _G. C. Greubel_, Nov 03 2019
%t A026801 Rest@CoefficientList[Series[x^8/QPochhammer[x^8, x], {x, 0, 75}], x] (* _G. C. Greubel_, Nov 03 2019 *)
%o A026801 (PARI) my(x='x+O('x^70)); concat(vector(7), Vec(x^8/prod(m=0,80, 1-x^(m+8)))) \\ _G. C. Greubel_, Nov 03 2019
%o A026801 (Magma) R