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 A330787 Triangle read by rows: T(n,k) is the number of strict multiset partitions of normal multisets of size n into k blocks, where a multiset is normal if it spans an initial interval of positive integers. 1
 1, 2, 1, 4, 8, 1, 8, 32, 18, 1, 16, 124, 140, 32, 1, 32, 444, 888, 432, 50, 1, 64, 1568, 5016, 4196, 1060, 72, 1, 128, 5440, 26796, 34732, 15064, 2224, 98, 1, 256, 18768, 138292, 262200, 174240, 44348, 4172, 128, 1, 512, 64432, 698864, 1870840, 1781884, 692668, 112424, 7200, 162, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..1275 (first 50 rows) EXAMPLE Triangle begins: 1; 2, 1; 4, 8, 1; 8, 32, 18, 1; 16, 124, 140, 32, 1; 32, 444, 888, 432, 50, 1; 64, 1568, 5016, 4196, 1060, 72, 1; 128, 5440, 26796, 34732, 15064, 2224, 98, 1; ... The T(3,1) = 4 multiset partitions are {{1,1,1}}, {{1,1,2}}, {{1,2,2}}, {{1,2,3}}. The T(3,2) = 8 multiset partitions are {{1},{1,1}}, {{1},{2,2}}, {{2},{1,2}}, {{1},{1,2}}, {{2},{1,1}}, {{1},{2,3}}, {{2},{1,3}}, {{3},{1,2}}. The T(3,3) = 1 multiset partition is {{1},{2},{3}}. MATHEMATICA B[n_, k_] := Sum[Binomial[r, k] (-1)^(r-k), {r, k, n}]; row[n_] := Sum[B[n, j] SeriesCoefficient[ Product[(1 + x^k y)^Binomial[k + j - 1, j - 1], {k, 1, n}], {x, 0, n}], {j, 1, n}]/y + O[y]^n // CoefficientList[#, y]&; Array[row, 10] // Flatten (* Jean-François Alcover, Dec 17 2020, after Andrew Howroyd *) PROG (PARI) \\ here B(n, k) is A239473(n, k) B(n, k)={sum(r=k, n, binomial(r, k)*(-1)^(r-k))} Row(n)={Vecrev(sum(j=1, n, B(n, j)*polcoef(prod(k=1, n, (1 + x^k*y + O(x*x^n))^binomial(k+j-1, j-1)), n))/y)} { for(n=1, 10, print(Row(n))) } CROSSREFS Row sums are A317776. Column 1 is A000079(n-1). Main diagonal is A000012. Cf. A317532, A327116. Sequence in context: A208917 A161381 A220579 * A128412 A221660 A221062 Adjacent sequences: A330784 A330785 A330786 * A330788 A330789 A330790 KEYWORD nonn,tabl AUTHOR Andrew Howroyd, Dec 31 2019 STATUS approved

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Last modified March 22 20:34 EDT 2023. Contains 361433 sequences. (Running on oeis4.)