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

0,3

Links

Table of n, a(n) for n=0..39.

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

Formula

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

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 *)

Crossrefs

Cf. A008763, A001993, A070557, A070558.

Sequence in context: A233758 A301653 A253769 * A320788 A000990 A129361

Adjacent sequences: A070556 A070557 A070558 * A070560 A070561 A070562

Keyword

nonn

Author

N. J. A. Sloane, May 07 2002

Status

approved