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A070558 Number of two-rowed partitions of length 5. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
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.
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
Sequence in context: A267151 A209008 A032279 * A233758 A301653 A253769
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, May 07 2002
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)