%I #15 Apr 05 2016 01:00:33
%S 1,1,3,5,10,16,28,42,68,100,151,215,312,432,605,821,1117,1485,1977,
%T 2581,3371,4335,5566,7060,8938,11196,13994,17338,21426,26280,32152,
%U 39074,47369,57093,68637,82097,97955,116339,137849,162665,191507
%N Number of two-rowed partitions of length 5.
%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.
%H L. Colmenarejo, <a href="http://arxiv.org/abs/1604.00803">Combinatorics on several families of Kronecker coefficients related to plane partitions</a>, arXiv:1604.00803 [math.CO], 2016. See Table 1 p. 5.
%F G.f.: 1/((1-x)*((1-x^2)*...*(1-x^m))^2*(1-x^(m+1))) for m = 5.
%p a:= n-> (Matrix(35, (i,j)-> if (i=j-1) then 1 elif j=1 then [1, 2, 0, -1, -3, -2, -2, 3, 7, 5, 1, -4, -8, -11, -1, 5, 9, 9, 5, -1, -11, -8, -4, 1, 5, 7, 3, -2, -2, -3, -1, 0, 2, 1, -1][i] else 0 fi)^n)[1,1]: seq(a(n), n=0..40); # _Alois P. Heinz_, Jul 31 2008
%t m = 5; n = 45; 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, A070559.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, May 07 2002