OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows)
EXAMPLE
The T(3,2) = 8 multiset partitions:
{{1},{1,1}}
{{1},{2,2}}
{{2},{1,2}}
{{1},{1,2}}
{{2},{1,1}}
{{1},{2,3}}
{{2},{1,3}}
{{3},{1,2}}
Triangle begins:
1
2 2
4 8 4
8 34 26 8
16 124 168 76 16
32 448 962 674 208 32
...
MATHEMATICA
sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}];
mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]];
allnorm[n_]:=Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1];
Table[Length[Select[Join@@mps/@allnorm[n], Length[#]==k&]], {n, 7}, {k, n}]
PROG
(PARI) \\ here B(n, k) is A239473(n, k).
B(n, k)={sum(r=k, n, binomial(r, k)*(-1)^(r-k))}
Row(n)={Vecrev(sum(j=1, n, B(n, j)*polcoef(1/prod(k=1, n, (1 - x^k*y + O(x*x^n))^binomial(k+j-1, j-1)), n))/y)}
{ for(n=1, 10, print(Row(n))) } \\ Andrew Howroyd, Dec 31 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Jul 30 2018
EXTENSIONS
Terms a(29) and beyond from Andrew Howroyd, Dec 31 2019
STATUS
approved