OFFSET
1,2
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1275 (rows 1..50)
EXAMPLE
The T(3,2) = 6 multiset partitions are {{1},{1,1}}, {{1},{1,2}}, {{2},{1,1}}, {{1},{2,3}}, {{2},{1,3}}, {{3},{1,2}}.
Triangle begins:
1
2 2
3 6 3
5 21 16 5
7 52 72 32 7
11 141 306 216 65 11
15 327 1113 1160 512 113 15
...
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]]]];
strnorm[n_]:=Flatten[MapIndexed[Table[#2, {#1}]&, #]]&/@IntegerPartitions[n];
Table[Length[Select[Join@@mps/@strnorm[n], Length[#]==k&]], {n, 6}, {k, n}]
PROG
(PARI)
EulerT(v)={Vec(exp(x*Ser(dirmul(v, vector(#v, n, 1/n))))-1, -#v)}
D(p, n)={my(v=vector(n)); for(i=1, #p, v[p[i]]++); my(u=EulerT(v)); Vec(1/prod(k=1, n, 1 - u[k]*x^k + O(x*x^n))-1, -n)/prod(i=1, #v, i^v[i]*v[i]!)}
U(m, n)={my(s=0); forpart(p=m, s+=D(p, n)); s}
M(n)={Mat(vector(n, k, (U(k, n)-U(k-1, n))~))}
{ my(A=M(8)); for(n=1, #A~, print(A[n, 1..n])) } \\ Andrew Howroyd, Dec 30 2020
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Aug 06 2018
EXTENSIONS
Terms a(46) and beyond from Andrew Howroyd, Dec 30 2020
STATUS
approved