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%I #12 Jul 17 2015 08:23:38
%S 1,1,3,5,10,16,29,44,72,108,166,241,357,504,720,998,1386,1882,2559,
%T 3413,4551,5981,7842,10162,13138,16811,21454,27150,34251,42898,53570,
%U 66464,82221,101146,124057,151404,184261,223235,269723,324578
%N Number of two-rowed partitions of length 6.
%H G. E. Andrews, <a href="http://dx.doi.org/10.1007/PL00001284">MacMahon's Partition Analysis II: Fundamental Theorems</a>, Annals Combinatorics, 4 (2000), 327-338.
%F G.f.: 1/((1-x)*((1-x^2)*...*(1-x^m))^2*(1-x^(m+1))) for m = 6.
%p a:= n-> (Matrix(48, (i,j)-> if (i=j-1) then 1 elif j=1 then [1, 2, 0, -1, -3, -1, -2, 0, 5, 6, 5, 1, -5, -11, -9, -7, 2, 9, 15, 16, 4, -5, -13, -16, -13, -5, 4, 16, 15, 9, 2, -7, -9, -11, -5, 1, 5, 6, 5, 0, -2, -1, -3, -1, 0, 2, 1, -1][i] else 0 fi)^n)[1,1]: seq(a(n), n=0..39); # _Alois P. Heinz_, Jul 31 2008
%t m = 6; n = 40; gf = 1/((1-x)*Product[1-x^k, {k, 2, m}]^2*(1-x^(m+1))) + O[x]^n; CoefficientList[gf, x] (* _Jean-François Alcover_, Jul 17 2015 *)
%Y Cf. A008763, A001993, A070557, A070558.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, May 07 2002
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