OFFSET
0,9
COMMENTS
Also the number of non-isomorphic multiset partitions of weight n with k parts and k vertices, where the weight of a multiset partition is the sum of sizes of its parts. - Gus Wiseman, Nov 18 2018
LINKS
Andrew Howroyd, Table of n, a(n) for n = 0..1325 (rows 0..50)
EXAMPLE
Triangle begins:
1
0 1
0 1 1
0 1 2 1
0 1 6 3 1
0 1 9 13 3 1
0 1 17 38 20 3 1
0 1 23 97 82 23 3 1
0 1 36 217 311 126 24 3 1
0 1 46 453 968 624 151 24 3 1
0 1 65 868 2825 2637 933 162 24 3 1
MATHEMATICA
(* See A318795 for M[m, n, k]. *)
T[n_, k_] := M[k, k, n] - 2 M[k, k-1, n] + M[k-1, k-1, n];
Table[T[n, k], {n, 1, 11}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 24 2018, from PARI *)
PROG
(PARI) \\ See A318795 for M.
T(n, k) = if(k==0, n==0, M(k, k, n) - 2*M(k, k-1, n) + M(k-1, k-1, n));
(PARI) \\ See A340652 for G.
T(n)={[Vecrev(p) | p<-Vec(1 + sum(k=1, n, y^k*(polcoef(G(k, n, n, y), k, y) - polcoef(G(k-1, n, n, y), k, y))))]}
{ my(A=T(10)); for(i=1, #A, print(A[i])) } \\ Andrew Howroyd, Jan 16 2024
CROSSREFS
Row sums are A319616.
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Nov 14 2018
EXTENSIONS
Column k=0 inserted by Andrew Howroyd, Jan 17 2024
STATUS
approved