A070557 Number of two-rowed partitions of length 4.

1, 1, 3, 5, 10, 15, 26, 38, 60, 85, 125, 172, 243, 325, 442, 580, 767, 986, 1275, 1612, 2045, 2548, 3179, 3910, 4812, 5849, 7109, 8554, 10285, 12259, 14599, 17255, 20372, 23895, 27991, 32603, 37925, 43890, 50725, 58361, 67053, 76727, 87678, 99825, 113503

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

Crossrefs

Cf. A008763, A001993, A070558, A070559.

Programs

Maple

a:= n-> (Matrix(24, (i,j)-> if (i=j-1) then 1 elif j=1 then [1, 2, 0, -1, -4, -2, 1, 5, 6, 0, -4, -6, -4, 0, 6, 5, 1, -2, -4, -1, 0, 2, 1, -1][i] else 0 fi)^n)[1,1]: seq (a(n), n=0..50); # Alois P. Heinz, Jul 31 2008

Mathematica

m = 4; 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 *)

Formula

G.f.: 1/((1-x)*((1-x^2)*...*(1-x^m))^2*(1-x^(m+1))) for m = 4.