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 A296122 Number of twice-partitions of n with no repeated partitions. 25
 1, 1, 2, 5, 10, 20, 40, 77, 157, 285, 552, 1018, 1921, 3484, 6436, 11622, 21082, 37550, 67681, 119318, 211792, 372003, 653496, 1137185, 1986234, 3429650, 5935970, 10205907, 17537684, 29958671, 51189932, 86967755, 147759421, 249850696, 422123392, 710495901 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) is the number of sequences of distinct integer partitions whose sums are weakly decreasing and add up to n. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..1000 EXAMPLE The a(4) = 10 twice-partitions: (4), (31), (22), (211), (1111), (3)(1), (21)(1), (111)(1), (2)(11), (11)(2). MAPLE b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(j!* binomial(combinat[numbpart](i), j)*b(n-i*j, i-1), j=0..n/i))) end: a:= n-> b(n\$2): seq(a(n), n=0..40); # Alois P. Heinz, Dec 06 2017 MATHEMATICA Table[Length[Join@@Table[Select[Tuples[IntegerPartitions/@p], UnsameQ@@#&], {p, IntegerPartitions[n]}]], {n, 15}] (* Second program: *) b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[j!* Binomial[PartitionsP[i], j]*b[n - i*j, i - 1], {j, 0, n/i}]]]; a[n_] := b[n, n]; a /@ Range[0, 40] (* Jean-François Alcover, May 19 2021, after Alois P. Heinz *) CROSSREFS Cf. A000009, A000041, A047968, A063834, A261049, A273873, A279375, A295279, A296121. Sequence in context: A068034 A222082 A327287 * A293324 A284904 A084215 Adjacent sequences: A296119 A296120 A296121 * A296123 A296124 A296125 KEYWORD nonn AUTHOR Gus Wiseman, Dec 05 2017 EXTENSIONS a(15)-a(34) from Robert G. Wilson v, Dec 06 2017 STATUS approved

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Last modified September 22 14:29 EDT 2023. Contains 365531 sequences. (Running on oeis4.)