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A070557 Number of two-rowed partitions of length 4. 3
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified August 24 16:21 EDT 2019. Contains 326295 sequences. (Running on oeis4.)