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
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Oct 29 2018
EXTENSIONS
Terms a(56) and beyond from Andrew Howroyd, Jan 11 2024
STATUS
approved