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 A323580 Number of ways to fill a Young diagram with positive integers summing to n such that the rows are weakly decreasing and the columns are weakly increasing. 3
 1, 1, 3, 6, 13, 23, 45, 76, 136, 225, 381, 611, 1001, 1570, 2489, 3842, 5948, 9022, 13714, 20501, 30649, 45262, 66721, 97393, 141888, 204993 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..25. nLab, Young Diagram. EXAMPLE The a(5) = 23 tableaux: 5 41 32 311 221 2111 11111 . 1 2 11 21 11 111 111 1111 4 3 3 2 21 2 11 1 . 1 1 11 11 111 1 2 1 11 1 3 2 2 1 1 . 1 11 1 1 1 1 2 1 . 1 1 1 1 1 MATHEMATICA primeMS[n_]:=If[n==1, {}, Flatten[Cases[FactorInteger[n], {p_, k_}:>Table[PrimePi[p], {k}]]]]; facs[n_]:=If[n<=1, {{}}, Join@@Table[Map[Prepend[#, d]&, Select[facs[n/d], Min@@#>=d&]], {d, Rest[Divisors[n]]}]]; Table[Sum[Length[Select[Reverse/@Sort/@Map[primeMS, facs[y], {2}], And@@(GreaterEqual@@@Transpose[PadRight[#]])&]], {y, Times@@Prime/@#&/@IntegerPartitions[n]}], {n, 10}] CROSSREFS Cf. A000085, A000219, A003293, A114736, A138178, A299968, A323436, A323437, A323438, A323439, A323581. Sequence in context: A308747 A022811 A295730 * A002799 A285263 A162426 Adjacent sequences: A323577 A323578 A323579 * A323581 A323582 A323583 KEYWORD nonn,more AUTHOR Gus Wiseman, Jan 18 2019 STATUS approved

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Last modified August 12 16:35 EDT 2024. Contains 375113 sequences. (Running on oeis4.)