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A075196
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Table T(n,k) by antidiagonals. Partitions of n balls of k colors.
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3
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1, 2, 2, 3, 6, 3, 4, 12, 14, 5, 5, 20, 38, 33, 7, 6, 30, 80, 117, 70, 11, 7, 42, 145, 305, 330, 149, 15, 8, 56, 238, 660, 1072, 906, 298, 22, 9, 72, 364, 1260, 2777, 3622, 2367, 591, 30, 10, 90, 528, 2198, 6174, 11160, 11676, 6027, 1132, 42, 11, 110, 735, 3582
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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Alois P. Heinz, Rows n = 1..141, flattened
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EXAMPLE
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1, 2, 3, 4, 5, ...
2, 6, 12, 20, 30, ...
3, 14, 38, 80, 145, ...
5, 33, 117, 305, 660, ...
7, 70, 330, 1072, 2777, ...
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MAPLE
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with (numtheory):
A:= proc(n, k) option remember; local d, j;
`if`(n=0, 1, add(add(d*binomial(d+k-1, k-1),
d=divisors(j)) *A(n-j, k), j=1..n)/n)
end:
seq (seq (A(n, 1+d-n), n=1..d), d=1..12); # Alois P. Heinz, Sep 26 2012
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MATHEMATICA
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Transpose[Table[nn=6; p=Product[1/(1- x^i)^Binomial[i+n, n], {i, 1, nn}]; Drop[CoefficientList[Series[p, {x, 0, nn}], x], 1], {n, 0, nn}]]//Grid (* Geoffrey Critzer, Sep 27 2012 *)
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CROSSREFS
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Columns 1-3: A000041, A005380, A217093.
Rows 1-2: A000027, A002378.
Main diagonal: A075197.
Sequence in context: A047662 A183474 A210220 * A196912 A197079 A208340
Adjacent sequences: A075193 A075194 A075195 * A075197 A075198 A075199
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KEYWORD
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nonn,tabl
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AUTHOR
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Christian G. Bower, Sep 07 2002
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STATUS
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approved
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