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A227579
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Number of lattice paths from {n}^n to {0}^n using steps that decrement one component such that for each point (p_1,p_2,...,p_n) we have p_1<=p_2<=...<=p_n.
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2
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1, 1, 5, 290, 456033, 36470203156, 237791136700913751, 184570140930218389159747070, 23408169635197679203800470649923362577, 637028433009539403532335279417025047587902906655768, 4725612998324981086891784010767387049970117446517002416810380479702
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OFFSET
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0,3
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LINKS
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EXAMPLE
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a(2) = 5: [(2,2),(0,2),(0,0)], [(2,2),(0,2),(0,1),(0,0)], [(2,2),(1,2),(0,2),(0,0)], [(2,2),(1,2),(0,2),(0,1),(0,0)], [(2,2),(1,2),(1,1),(0,1),(0,0)].
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MAPLE
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b:= proc(l) option remember; `if`(l[-1]=0, 1, add(add(b(subsop(
i=j, l)), j=`if`(i=1, 0, l[i-1])..l[i]-1), i=1..nops(l)))
end:
a:= n-> `if`(n=0, 1, b([n$n])):
seq(a(n), n=0..9);
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MATHEMATICA
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b[l_] := b[l] = If[l[[-1]] == 0, 1, Sum[Sum[b[ReplacePart[l, i -> j]], {j, If[i == 1, 0, l[[i - 1]]], l[[i]] - 1}], {i, 1, Length[l]}]];
a[n_] := If[n == 0, 1, b[Table[n, {n}]]];
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CROSSREFS
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KEYWORD
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nonn,hard
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AUTHOR
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STATUS
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approved
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