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A097965
Number of compositions (ordered partitions) of n into n parts, allowing zeros, with distinct nonzero parts.
1
1, 2, 9, 16, 45, 186, 343, 848, 1809, 8290, 13431, 33672, 66157, 143066, 591165, 966016, 2180913, 4281570, 8776423, 15865400, 67586841, 101053282, 226690047, 420479952, 845781625, 1476079826, 2830894353, 10479645568, 15758982597, 33145324410, 60465162751
OFFSET
1,2
LINKS
MAPLE
b:= proc(n, i) option remember; `if`(n=0, [1],
`if`(n>i*(i+1)/2, [], zip((x, y)->x+y, b(n, i-1),
`if`(i>n, [], [0, b(n-i, i-1)[]]), 0)))
end:
a:= proc(n) local l; l:= b(n$2);
add(l[i+1]*i!*binomial(n, i), i=1..nops(l)-1)
end:
seq (a(n), n=1..40); # Alois P. Heinz, Nov 20 2012
MATHEMATICA
zip[f_, x_List, y_List, z_] := With[{m = Max[Length[x], Length[y]]}, Thread[f[PadRight[x, m, z], PadRight[y, m, z]]]]; b[n_, i_] := b[n, i] = If[n == 0, {1}, If[n > i*(i+1)/2, {}, zip[Plus, b[n, i-1], If[i>n, {}, Join[{0}, b[n-i, i-1]]], 0]]]; a[n_] := Module[{l}, l = b[n, n]; Sum[l[[i+1]]*i!*Binomial[n, i], {i, 1, Length[l]-1}]]; Table[a[n], {n, 1, 40}] (* Jean-François Alcover, Jan 29 2014, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A304907 A237282 A178440 * A304974 A075645 A185252
KEYWORD
nonn
AUTHOR
Vladeta Jovovic, Sep 21 2004
STATUS
approved