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A321615
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Triangle read by rows: T(n,k) is the number of k X k integer matrices with sum of elements n, with no zero rows or columns, up to row and column permutation.
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5
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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, 0, 1, 80, 1585, 7394, 10098, 4942, 1132, 165, 24, 3, 1
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OFFSET
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0,9
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COMMENTS
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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
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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T[n_, k_] := M[k, k, n] - 2 M[k, k-1, n] + M[k-1, k-1, n];
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PROG
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T(n, k) = if(k==0, n==0, M(k, k, n) - 2*M(k, k-1, n) + M(k-1, k-1, n));
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
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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