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 A322439 Number of ordered pairs of integer partitions of n where no part of the first is greater than any part of the second. 7
 1, 1, 3, 5, 11, 15, 33, 42, 82, 114, 195, 258, 466, 587, 954, 1317, 2021, 2637, 4124, 5298, 7995, 10565, 15075, 19665, 28798, 36773, 51509, 67501, 93060, 119299, 165589, 209967, 285535, 366488, 487536, 622509, 833998, 1048119, 1380410, 1754520, 2291406, 2876454 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..10000 FORMULA a(n) = Sum_{k = 1...n} A026820(n, k) * A026794(n, k). EXAMPLE The a(5) = 15 pairs of integer partitions:       (5)|(5)      (41)|(5)      (32)|(5)     (311)|(5)     (221)|(5)     (221)|(32)    (2111)|(5)    (2111)|(32)   (11111)|(5)   (11111)|(41)   (11111)|(32)   (11111)|(311)   (11111)|(221)   (11111)|(2111)   (11111)|(11111) MAPLE g:= proc(n, i) option remember; `if`(n=0 or i=1, 1,       g(n, i-1) +g(n-i, min(i, n-i)))     end: b:= proc(n, i) option remember; `if`(n=0, 1,       `if`(i>n, 0, b(n, i+1)+b(n-i, i)))     end: a:= proc(n) option remember; `if`(n=0, 1,       add(g(n, i)*b(n-i, i), i=1..n))     end: seq(a(n), n=0..50);  # Alois P. Heinz, Dec 09 2018 MATHEMATICA Table[Length[Select[Tuples[IntegerPartitions[n], 2], Max@@First[#]<=Min@@Last[#]&]], {n, 20}] CROSSREFS Cf. A026794, A026820, A265947, A285573, A317144, A318915, A322435, A322436, A322440, A322441, A322442. Sequence in context: A092929 A138879 A318915 * A018313 A219039 A074820 Adjacent sequences:  A322436 A322437 A322438 * A322440 A322441 A322442 KEYWORD nonn AUTHOR Gus Wiseman, Dec 08 2018 STATUS approved

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Last modified May 29 20:42 EDT 2020. Contains 334710 sequences. (Running on oeis4.)