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 A321615 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. 5
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 Columns k=0..3 are A000007, A000012, A054974, A054975. Row sums are A319616. Cf. A007716, A048291, A054976, A057149, A057150, A104601, A120732, A318795, A320808. Sequence in context: A291584 A352451 A349618 * A011126 A266854 A326882 Adjacent sequences: A321612 A321613 A321614 * A321616 A321617 A321618 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Nov 14 2018 EXTENSIONS Column k=0 inserted by Andrew Howroyd, Jan 17 2024 STATUS approved

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Last modified June 12 12:44 EDT 2024. Contains 373331 sequences. (Running on oeis4.)