OFFSET
0,5
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..350
EXAMPLE
Triangle begins:
1
0 1
0 4 2
0 10 8 3
0 33 48 18 5
0 91 204 118 32 7
0 298 959 743 266 58 11
For example, row n = 3 counts the following multiset partitions:
{{111}} {{1}}{{11}} {{1}}{{1}}{{1}}
{{112}} {{1}}{{12}} {{1}}{{1}}{{2}}
{{123}} {{1}}{{23}} {{1}}{{2}}{{3}}
{{1}{11}} {{2}}{{11}}
{{1}{12}} {{1}}{{1}{1}}
{{1}{23}} {{1}}{{1}{2}}
{{2}{11}} {{1}}{{2}{3}}
{{1}{1}{1}} {{2}}{{1}{1}}
{{1}{1}{2}}
{{1}{2}{3}}
PROG
(PARI) \\ See links in A339645 for combinatorial species functions.
ColGf(k, n)={my(A=symGroupSeries(n)); OgfSeries(sCartProd(sExp(A), sSubstOp(polcoef(A, k, x)*x^k + O(x*x^n), sExp(A)) ))}
M(n, m=n)={Mat(vector(m+1, k, Col(ColGf(k-1, n), -(n+1))))}
{ my(A=M(10)); for(n=1, #A, print(A[n, 1..n])) } \\ Andrew Howroyd, Jan 17 2023
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Dec 19 2019
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Jan 17 2023
STATUS
approved