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

0,3

Links

Table of n, a(n) for n=0..44.

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 = 4.

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 *)

Crossrefs

Cf. A008763, A001993, A070558, A070559.

Sequence in context: A308826 A090491 A126728 * A225751 A264397 A254346

Adjacent sequences: A070554 A070555 A070556 * A070558 A070559 A070560

Keyword

nonn

Author

N. J. A. Sloane, May 07 2002

Status

approved