OFFSET
0,3
COMMENTS
If we form a multiorder by treating integer partitions (a,...,z) as multiarrows GCD(a, ..., z) <= {z, ..., a}, then a(n) is the number of triangles of weight n.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1000
EXAMPLE
The a(4) = 18 ordered multiset partitions:
{{4}} {{1,3}} {{2,2}} {{1,1,2}} {{1,1,1,1}}
{{1},{3}} {{2},{2}} {{1},{1,2}} {{1},{1,1,1}}
{{1,2},{1}} {{1,1,1},{1}}
{{1,1},{2}} {{1,1},{1,1}}
{{1},{1},{2}} {{1},{1},{1,1}}
{{1},{1,1},{1}}
{{1,1},{1},{1}}
{{1},{1},{1},{1}}
PROG
(PARI) \\ here B(n) is A000837 as vector.
B(n) = {dirmul(vector(n, k, moebius(k)), vector(n, k, numbpart(k)))}
seq(n) ={my(p=x*Ser(B(n))); Vec(1/prod(g=1, n, 1 - subst(p + O(x*x^(n\g)), x, x^g)))} \\ Andrew Howroyd, Jan 16 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Sep 07 2018
EXTENSIONS
a(0)=1 prepended and terms a(11) and beyond from Andrew Howroyd, Jan 16 2023
STATUS
approved