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A321194
Regular triangle where T(n,k) is the number of non-isomorphic multiset partitions of weight n with k connected components.
15
1, 3, 1, 6, 3, 1, 17, 12, 3, 1, 40, 35, 12, 3, 1, 125, 112, 45, 12, 3, 1, 354, 347, 148, 45, 12, 3, 1, 1159, 1122, 512, 163, 45, 12, 3, 1, 3774, 3651, 1724, 572, 163, 45, 12, 3, 1, 13113, 12320, 5937, 2020, 593, 163, 45, 12, 3, 1, 46426, 42407, 20492, 7117, 2110, 593, 163, 45, 12, 3, 1
OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)
FORMULA
O.g.f.: Product 1/(1 - t*x^n)^A007718(n).
EXAMPLE
Triangle begins:
1
3 1
6 3 1
17 12 3 1
40 35 12 3 1
125 112 45 12 3 1
354 347 148 45 12 3 1
1159 1122 512 163 45 12 3 1
3774 3651 1724 572 163 45 12 3 1
13113 12320 5937 2020 593 163 45 12 3 1
The fourth row counts the following non-isomorphic multiset partitions.
{{1,1,1,1}} {{1,1},{2,2}} {{1},{2},{3,3}} {{1},{2},{3},{4}}
{{1,1,2,2}} {{1},{2,2,2}} {{1},{2},{3,4}}
{{1,2,2,2}} {{1},{2,3,3}} {{1},{2},{3},{3}}
{{1,2,3,3}} {{1,2},{3,3}}
{{1,2,3,4}} {{1},{2,3,4}}
{{1},{1,1,1}} {{1,2},{3,4}}
{{1,1},{1,1}} {{1},{1},{2,2}}
{{1},{1,2,2}} {{1},{1},{2,3}}
{{1,2},{1,2}} {{1},{2},{2,2}}
{{1,2},{2,2}} {{1},{3},{2,3}}
{{1,3},{2,3}} {{1},{1},{2},{2}}
{{2},{1,2,2}} {{1},{2},{2},{2}}
{{3},{1,2,3}}
{{1},{1},{1,1}}
{{1},{2},{1,2}}
{{2},{2},{1,2}}
{{1},{1},{1},{1}}
CROSSREFS
First column is A007718. Row sums are A007716.
Sequence in context: A094504 A107884 A185628 * A158822 A353924 A226132
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Oct 29 2018
EXTENSIONS
Terms a(56) and beyond from Andrew Howroyd, Jan 11 2024
STATUS
approved