OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..207 (first 50 rows)
FORMULA
T(n,d) = A219727(d, n/d). - Andrew Howroyd, Jan 11 2020
EXAMPLE
Triangle begins:
1
2 2
5 3
15 9 5
52 7
203 66 31 11
877 15
4140 712 109 22
21147 686 30
115975 10457 339 42
678570 56
4213597 198091 27036 6721 1043 77
For example, row 4 counts the following multiset partitions.
{{1,2,3,4}} {{1,1,2,2}} {{1,1,1,1}}
{{1},{2,3,4}} {{1},{1,2,2}} {{1},{1,1,1}}
{{1,2},{3,4}} {{1,1},{2,2}} {{1,1},{1,1}}
{{1,3},{2,4}} {{1,2},{1,2}} {{1},{1},{1,1}}
{{1,4},{2,3}} {{2},{1,1,2}} {{1},{1},{1},{1}}
{{2},{1,3,4}} {{1},{1},{2,2}}
{{3},{1,2,4}} {{1},{2},{1,2}}
{{4},{1,2,3}} {{2},{2},{1,1}}
{{1},{2},{3,4}} {{1},{1},{2},{2}}
{{1},{3},{2,4}}
{{1},{4},{2,3}}
{{2},{3},{1,4}}
{{2},{4},{1,3}}
{{3},{4},{1,2}}
{{1},{2},{3},{4}}
MATHEMATICA
u[n_, k_]:=u[n, k]=If[n==1, 1, Sum[u[n/d, d], {d, Select[Rest[Divisors[n]], #<=k&]}]];
Table[Table[u[Array[Prime, n/d, 1, Times]^d, Array[Prime, n/d, 1, Times]^d], {d, Divisors[n]}], {n, 10}]
PROG
(PARI) \\ needs T(n, k) from A219727.
Row(n)={[T(d, n/d) | d<-divisors(n)]}
{ for(n=1, 12, print(Row(n))) } \\ Andrew Howroyd, Jan 11 2020
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Gus Wiseman, Dec 26 2018
STATUS
approved