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A229267
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Number of lattice paths from {n}^n to {0}^n using steps that decrement one component or all components by 1.
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3
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1, 1, 13, 2371, 67982041, 629799991355641, 2672932604015450235911761, 7364217994146042440421602767480184881, 18165821273625565354157327818616137066973745155992321, 53130704578476340997304138835621075610747224340706918846011664495415681
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{j=0..n} multinomial(n+(n-1)*j; n-j, {j}^n) for n>1, a(0) = a(1) = 1.
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EXAMPLE
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a(2) = 3*3 + 2*2 = 13:
. (0,2)
. / \
. (1,2)-------(0,1)
. / \ / \
(2,2)-------(1,1)-------(0,0)
. \ / \ /
. (2,1)-------(1,0)
. \ /
. (2,0)
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MAPLE
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with(combinat):
a:= n-> `if`(n<2, 1, add(multinomial(n+(n-1)*j, n-j, j$n), j=0..n)):
seq(a(n), n=0..10);
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MATHEMATICA
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multinomial[n_, k_List] := n!/Times @@ (k!); a[n_] := If[n < 2, 1, Sum[multinomial[n+(n-1)*j, Join[{n-j}, Array[j&, n]]], {j, 0, n}]]; Table[a[n], {n, 0, 10}] (* Jean-François Alcover, Dec 27 2013, translated from Maple *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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