A070559 Number of two-rowed partitions of length 6.

1, 1, 3, 5, 10, 16, 29, 44, 72, 108, 166, 241, 357, 504, 720, 998, 1386, 1882, 2559, 3413, 4551, 5981, 7842, 10162, 13138, 16811, 21454, 27150, 34251, 42898, 53570, 66464, 82221, 101146, 124057, 151404, 184261, 223235, 269723, 324578

Offset: 0

Author

N. J. A. Sloane, May 07 2002

Keywords

• nonn

Links

• G. E. Andrews, MacMahon's Partition Analysis II: Fundamental Theorems, Annals Combinatorics, 4 (2000), 327-338.

Crossrefs

Cf. A008763, A001993, A070557, A070558.

Programs

Maple

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

Mathematica

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 *)

Formula

G.f.: 1/((1-x)*((1-x^2)*...*(1-x^m))^2*(1-x^(m+1))) for m = 6.