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A104778 Table of values with shape sequence A000041 related to involutions and multinomials. Also column sums of the Kostka matrices associated with the partitions (in Abramowitz & Stegun ordering). 6
1, 1, 1, 2, 1, 2, 4, 1, 2, 3, 5, 10, 1, 2, 3, 5, 7, 13, 26, 1, 2, 3, 4, 5, 8, 11, 14, 20, 38, 76, 1, 2, 3, 4, 5, 8, 10, 13, 14, 23, 32, 42, 60, 116, 232, 1, 2, 3, 4, 5, 5, 8, 11, 14, 17, 14, 24, 30, 40, 56, 43, 73, 103, 136, 196, 382, 764, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Wouter Meeussen, Table of n, a(n) for n = 0..372

EXAMPLE

The 47 multinomials (corresponding to A005651(4)=47) can be distributed as in the following triangular array:

1

9 1

4 6 1

9 2 3 1

1 3 2 3 1

divide each term by

1

3 1

2 3 1

3 2 3 1

1 3 2 3 1

yielding

1

3 1

2 2 1

3 1 1 1

1 1 1 1 1

with column sums 10 5 3 2 1.

Therefore the fourth row of the table is 1 2 3 5 10

The initial rows are 1; 1; 1,2; 1,2,4; 1,2,3,5,10; 1,2,3,5,7,13,26; ...

MATHEMATICA

(*function 'kostka': see A178718*) aspartitions[n_] := Reverse /@ Sort[Sort /@ Partitions[n]]; asorder[n_] := rankpartition /@ Reverse /@ Sort[Sort /@ Partitions[n]]; Flatten[Table[Tr/@ Transpose[PadLeft[#, PartitionsP[k]] [[asorder[k]] ]&/@ kostka/@ aspartitions[k]], {k, 11}]]

CROSSREFS

Cf. A000041, A000085, A005651, A036038, A097522, A104707, A104778, A178718.

A001475 and A000085 are subsequences.

Sequence in context: A132082 A129644 A081517 * A292477 A081532 A174843

Adjacent sequences:  A104775 A104776 A104777 * A104779 A104780 A104781

KEYWORD

nonn,tabf,obsc

AUTHOR

Alford Arnold, Mar 24 2005

EXTENSIONS

I marked this as "obsc" since I cannot understand how the triangles are defined. - N. J. A. Sloane, Dec 26 2010; Corrected and edited by W. Meeussen, Jan 15 2012

STATUS

approved

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Last modified November 18 09:16 EST 2017. Contains 294879 sequences.