

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
Wouter Meeussen, Table of n, a(n), partition parts 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 Wouter Meeussen, Jan 15 2012


STATUS

approved



