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A027293 Triangular array T given by rows: P(n,k) = number of partitions of n that contain k as a part. +0
4
1, 1, 1, 2, 1, 1, 3, 2, 1, 1, 5, 3, 2, 1, 1, 7, 5, 3, 2, 1, 1, 11, 7, 5, 3, 2, 1, 1, 15, 11, 7, 5, 3, 2, 1, 1, 22, 15, 11, 7, 5, 3, 2, 1, 1, 30, 22, 15, 11, 7, 5, 3, 2, 1, 1, 42, 30, 22, 15, 11, 7, 5, 3, 2, 1, 1, 56, 42, 30, 22, 15, 11, 7, 5, 3, 2, 1, 1, 77 (list; table; graph; listen)
OFFSET

1,4

EXAMPLE

Triangle begins:

1

1 1

2 1 1

3 2 1 1

5 3 2 1 1

7 5 3 2 1 1

11 7 5 3 2 1 1

15 11 7 5 3 2 1 1

22 15 11 7 5 3 2 1 1

30 22 15 11 7 5 3 2 1 1

42 30 22 15 11 7 5 3 2 1 1

MATHEMATICA

(* first *) Needs["DiscreteMath`Combinatorica`"] (* then *) f[n_] := Block[{t = Flatten[Union /(AT) Partitions(AT)n]}, Table[Count[t, i], {i, n}]]; Array[f, 13] // Flatten.

CROSSREFS

Every column of T is A000041.

Adjacent sequences: A027290 A027291 A027292 this_sequence A027294 A027295 A027296

Sequence in context: A093628 A114282 A112739 this_sequence A104762 A098805 A049286

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling (ck6(AT)evansville.edu)

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Last modified October 10 20:39 EDT 2008. Contains 144831 sequences.


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