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 A216221 Triangular array read by rows. T(n,k) is the number of partitions of n (using 1 type of part 1, 2 types of part 2, ..., i types of part i, ...) that have exactly k distinct parts. 0
 1, 3, 4, 2, 7, 6, 6, 17, 1, 12, 29, 7, 8, 55, 23, 15, 84, 58, 3, 13, 122, 134, 13, 18, 181, 249, 52, 12, 240, 464, 140, 3, 28, 321, 765, 348, 17, 14, 407, 1249, 746, 69, 24, 546, 1875, 1501, 220, 1, 24, 628, 2835, 2793, 586, 13, 31, 828, 4024, 4927, 1431, 56, 18, 940, 5707, 8331, 3123, 215, 39, 1211, 7741, 13520, 6436, 650, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row sums = A000219. LINKS Table of n, a(n) for n=1..73. P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; page 171 FORMULA O.g.f.: Product_{i>=1} (1 + y*x^i/(1-x^i))^i. EXAMPLE 1, 3, 4, 2, 7, 6, 6, 17, 1, 12, 29, 7, 8, 55, 23, 15, 84, 58, 3, 13, 122, 134, 13, 18, 181, 249, 52, 12, 240, 464, 140, 3, 28, 321, 765, 348, 17, 14, 407, 1249, 746, 69, 24, 546, 1875, 1501, 220, 1 24, 628, 2835, 2793, 586, 13 T(4,2) = 6 because we have: 3+1, 3'+1, 3''+1, 2+2', 2+1+1, 2'+1+1. MATHEMATICA nn=15; f[list_]:=Select[list, #>0&]; Map[f, Drop[CoefficientList[Series[ Product[(1+y x^i/(1-x^i))^i, {i, 1, nn}], {x, 0, nn}], {x, y}], 1]]//Grid CROSSREFS Sequence in context: A205769 A166108 A255768 * A296431 A045901 A098003 Adjacent sequences: A216218 A216219 A216220 * A216222 A216223 A216224 KEYWORD nonn,tabf AUTHOR Geoffrey Critzer, Mar 13 2013 STATUS approved

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Last modified May 29 00:29 EDT 2024. Contains 372921 sequences. (Running on oeis4.)