A070558 Number of two-rowed partitions of length 5.

1, 1, 3, 5, 10, 16, 28, 42, 68, 100, 151, 215, 312, 432, 605, 821, 1117, 1485, 1977, 2581, 3371, 4335, 5566, 7060, 8938, 11196, 13994, 17338, 21426, 26280, 32152, 39074, 47369, 57093, 68637, 82097, 97955, 116339, 137849, 162665, 191507

Offset

0,3

Links

Table of n, a(n) for n=0..40.

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

L. Colmenarejo, Combinatorics on several families of Kronecker coefficients related to plane partitions, arXiv:1604.00803 [math.CO], 2016. See Table 1 p. 5.

Formula

G.f.: 1/((1-x)*((1-x^2)*...*(1-x^m))^2*(1-x^(m+1))) for m = 5.

Maple

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

Mathematica

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 *)

Crossrefs

Cf. A008763, A001993, A070557, A070559.

Sequence in context: A267151 A209008 A032279 * A233758 A301653 A253769

Adjacent sequences: A070555 A070556 A070557 * A070559 A070560 A070561

Keyword

nonn

Author

N. J. A. Sloane, May 07 2002

Status

approved