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 A317532 Regular triangle read by rows: T(n,k) is the number of 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. 12
 1, 2, 2, 4, 8, 4, 8, 34, 26, 8, 16, 124, 168, 76, 16, 32, 448, 962, 674, 208, 32, 64, 1568, 5224, 5344, 2392, 544, 64, 128, 5448, 27336, 39834, 24578, 7816, 1376, 128, 256, 18768, 139712, 283864, 236192, 99832, 24048, 3392, 256, 512, 64448, 702496, 1960320, 2161602, 1186866, 370976, 70656, 8192, 512 (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 The T(3,2) = 8 multiset partitions: {{1},{1,1}} {{1},{2,2}} {{2},{1,2}} {{1},{1,2}} {{2},{1,1}} {{1},{2,3}} {{2},{1,3}} {{3},{1,2}} Triangle begins: 1 2 2 4 8 4 8 34 26 8 16 124 168 76 16 32 448 962 674 208 32 ... MATHEMATICA sps[{}]:={{}}; sps[set:{i_, ___}]:=Join@@Function[s, Prepend[#, s]&/@sps[Complement[set, s]]]/@Cases[Subsets[set], {i, ___}]; mps[set_]:=Union[Sort[Sort/@(#/.x_Integer:>set[[x]])]&/@sps[Range[Length[set]]]]; allnorm[n_]:=Function[s, Array[Count[s, y_/; y<=#]+1&, n]]/@Subsets[Range[n-1]+1]; Table[Length[Select[Join@@mps/@allnorm[n], Length[#]==k&]], {n, 7}, {k, n}] 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(1/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))) } \\ Andrew Howroyd, Dec 31 2019 CROSSREFS Row sums are A255906. Cf. A007716, A034691, A255397, A255903. Sequence in context: A213418 A317517 A300182 * A222659 A116694 A220810 Adjacent sequences: A317529 A317530 A317531 * A317533 A317534 A317535 KEYWORD nonn,tabl AUTHOR Gus Wiseman, Jul 30 2018 EXTENSIONS Terms a(29) and beyond from Andrew Howroyd, Dec 31 2019 STATUS approved

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Last modified September 18 03:51 EDT 2024. Contains 375995 sequences. (Running on oeis4.)