OFFSET
0,5
COMMENTS
The weight of a multiset partition is the sum of sizes of its parts. Weight is generally not the same as number of vertices.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
EXAMPLE
Triangle begins:
1
0 1
0 2 1
0 3 2 1
0 5 8 3 1
0 7 17 12 3 1
0 11 46 45 18 4 1
0 15 94 141 76 23 4 1
0 22 212 432 333 124 30 5 1
0 30 416 1231 1254 622 178 37 5 1
0 42 848 3346 4601 2914 1058 252 45 6 1
Non-isomorphic representatives of the multiset partitions counted in row 4:
{{1,1,1,1}} {{1,1,2,2}} {{1,2,3,3}} {{1,2,3,4}}
{{1},{1,1,1}} {{1,2,2,2}} {{1,3},{2,3}}
{{1,1},{1,1}} {{1},{1,2,2}} {{3},{1,2,3}}
{{1},{1},{1,1}} {{1,2},{1,2}}
{{1},{1},{1},{1}} {{1,2},{2,2}}
{{2},{1,2,2}}
{{1},{2},{1,2}}
{{2},{2},{1,2}}
PROG
(PARI) \\ Needs G(m, n) defined in A317533 (faster PARI).
InvEulerMTS(p)={my(n=serprec(p, x)-1, q=log(p), vars=variables(p)); sum(i=1, n, moebius(i)*substvec(q + O(x*x^(n\i)), vars, apply(v->v^i, vars))/i)}
T(n)={[Vecrev(p) | p <- Vec(1 + InvEulerMTS(y^n*G(n, n) + sum(k=0, n-1, y^k*(1 - y)*G(k, n))))]}
{ my(A=T(10)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Jan 15 2024
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Nov 27 2018
STATUS
approved