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 A120774 Number of ordered set partitions of [n] where equal-sized blocks are ordered with increasing least elements. 6
 1, 1, 2, 8, 31, 147, 899, 5777, 41024, 322488, 2749325, 25118777, 245389896, 2554780438, 28009868787, 323746545433, 3933023224691, 49924332801387, 661988844566017, 9138403573970063, 131043199040556235, 1949750421507432009, 30031656711776544610 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Old name was: Row sums of A179233. a(n) is the number of ways to linearly order the blocks in each set partition of {1,2,...,n} where two blocks are considered identical if they have the same number of elements. - Geoffrey Critzer, Sep 29 2011 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..525 EXAMPLE A179233 begins 1; 1; 1 1; 6 1 1; 8 3 18 1 1 ... with row sums 1, 1 2 8 31 147 ... a(3) = 8: 123, 1|23, 23|1, 2|13, 13|2, 3|12, 12|3, 1|2|3. - Alois P. Heinz, Apr 27 2017 MAPLE b:= proc(n, i, p) option remember; `if`(n=0 or i=1,       (p+n)!/n!, add(b(n-i*j, i-1, p+j)*combinat       [multinomial](n, n-i*j, i\$j)/j!^2, j=0..n/i))     end: a:= n-> b(n\$2, 0): seq(a(n), n=0..25);  # Alois P. Heinz, Apr 27 2017 MATHEMATICA f[{x_, y_}]:= x!^y y!;   Table[Total[Table[n!, {PartitionsP[n]}]/Apply[Times, Map[f, Map[Tally, Partitions[n]], {2}], 2] * Apply[Multinomial, Map[Last, Map[Tally, Partitions[n]], {2}], 2]], {n, 0, 20}]  (* Geoffrey Critzer, Sep 29 2011 *) CROSSREFS Cf. A000041, A032011, A049019, A096161, A096162, A196301. Row sums of A179233, A285824. Main diagonal of A327244. Sequence in context: A150827 A150828 A308336 * A261052 A128324 A264572 Adjacent sequences:  A120771 A120772 A120773 * A120775 A120776 A120777 KEYWORD easy,nonn AUTHOR Alford Arnold, Jul 12 2006 EXTENSIONS Leading 1 inserted, definition simplified by R. J. Mathar, Sep 28 2011 a(15) corrected, more terms, and new name (using Geoffrey Critzer's comment) from Alois P. Heinz, Apr 27 2017 STATUS approved

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Last modified February 22 18:03 EST 2020. Contains 332148 sequences. (Running on oeis4.)