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 A322786 Irregular triangle read by rows where if d|n then T(n,d) is the number of multiset partitions of a multiset with d copies of each integer from 1 to n/d. 3
 1, 2, 2, 5, 3, 15, 9, 5, 52, 7, 203, 66, 31, 11, 877, 15, 4140, 712, 109, 22, 21147, 686, 30, 115975, 10457, 339, 42, 678570, 56, 4213597, 198091, 27036, 6721, 1043, 77, 27644437, 101, 190899322, 4659138, 2998, 135, 1382958545, 1688360, 58616, 176 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Andrew Howroyd, Table of n, a(n) for n = 1..207 (first 50 rows) FORMULA T(n,d) = A001055(A002110(n/d)^d). T(n,d) = A219727(d, n/d). - Andrew Howroyd, Jan 11 2020 EXAMPLE Triangle begins: 1 2 2 5 3 15 9 5 52 7 203 66 31 11 877 15 4140 712 109 22 21147 686 30 115975 10457 339 42 678570 56 4213597 198091 27036 6721 1043 77 For example, row 4 counts the following multiset partitions. {{1,2,3,4}} {{1,1,2,2}} {{1,1,1,1}} {{1},{2,3,4}} {{1},{1,2,2}} {{1},{1,1,1}} {{1,2},{3,4}} {{1,1},{2,2}} {{1,1},{1,1}} {{1,3},{2,4}} {{1,2},{1,2}} {{1},{1},{1,1}} {{1,4},{2,3}} {{2},{1,1,2}} {{1},{1},{1},{1}} {{2},{1,3,4}} {{1},{1},{2,2}} {{3},{1,2,4}} {{1},{2},{1,2}} {{4},{1,2,3}} {{2},{2},{1,1}} {{1},{2},{3,4}} {{1},{1},{2},{2}} {{1},{3},{2,4}} {{1},{4},{2,3}} {{2},{3},{1,4}} {{2},{4},{1,3}} {{3},{4},{1,2}} {{1},{2},{3},{4}} MATHEMATICA u[n_, k_]:=u[n, k]=If[n==1, 1, Sum[u[n/d, d], {d, Select[Rest[Divisors[n]], #<=k&]}]]; Table[Table[u[Array[Prime, n/d, 1, Times]^d, Array[Prime, n/d, 1, Times]^d], {d, Divisors[n]}], {n, 10}] PROG (PARI) \\ needs T(n, k) from A219727. Row(n)={[T(d, n/d) | d<-divisors(n)]} { for(n=1, 12, print(Row(n))) } \\ Andrew Howroyd, Jan 11 2020 CROSSREFS Row sums are A322784. First column is A000110. Cf. A001055, A005176, A056239, A072774, A100778, A219727, A295193, A306017, A319190, A319612, A322784, A322785, A322787, A322788, A322792. Sequence in context: A147524 A113177 A344507 * A184243 A356891 A135281 Adjacent sequences: A322783 A322784 A322785 * A322787 A322788 A322789 KEYWORD nonn,tabf AUTHOR Gus Wiseman, Dec 26 2018 STATUS approved

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Last modified December 7 12:36 EST 2022. Contains 358656 sequences. (Running on oeis4.)