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 A209406 Triangular array read by rows: T(n,k) is the number of multisets of exactly k nonempty binary words with a total of n letters. 6
 2, 4, 3, 8, 8, 4, 16, 26, 12, 5, 32, 64, 44, 16, 6, 64, 164, 132, 62, 20, 7, 128, 384, 376, 200, 80, 24, 8, 256, 904, 1008, 623, 268, 98, 28, 9, 512, 2048, 2632, 1792, 870, 336, 116, 32, 10, 1024, 4624, 6624, 5040, 2632, 1117, 404, 134, 36, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Equivalently, T(n,k) is the number of partitions of the integer n with two types of 1's, four types of 2's, ..., 2^i types of i's...; having exactly k summands (of any type). Row sums = A034899. LINKS Alois P. Heinz, Rows n = 1..141, flattened FORMULA O.g.f.: Product_{i>=1} 1/(1-y*x^i)^(2^i). EXAMPLE :   2; :   4,    3; :   8,    8,    4; :  16,   26,   12,    5; :  32,   64,   44,   16,   6; :  64,  164,  132,   62,  20,   7; : 128,  384,  376,  200,  80,  24,   8; : 256,  904, 1008,  623, 268,  98,  28,  9; : 512, 2048, 2632, 1792, 870, 336, 116, 32, 10; MAPLE b:= proc(n, i, p) option remember; `if`(p>n, 0, `if`(n=0, 1,       `if`(min(i, p)<1, 0, add(b(n-i*j, i-1, p-j)*        binomial(2^i+j-1, j), j=0..min(n/i, p)))))     end: T:= (n, k)-> b(n\$2, k): seq(seq(T(n, k), k=1..n), n=1..14);  # Alois P. Heinz, Apr 13 2017 MATHEMATICA nn = 10; p[x_, y_] := Product[1/(1 - y x^i)^(2^i), {i, 1, nn}]; f[list_] := Select[lst, # > 0 &]; Map[f, Drop[CoefficientList[Series[p[x, y], {x, 0, nn}], {x, y}], 1]] // Flatten CROSSREFS Cf. A034899, A208741, A290222, A292506. Sequence in context: A067179 A318993 A188843 * A188706 A304408 A048767 Adjacent sequences:  A209403 A209404 A209405 * A209407 A209408 A209409 KEYWORD nonn,tabl AUTHOR Geoffrey Critzer, Mar 08 2012 STATUS approved

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Last modified April 8 14:52 EDT 2020. Contains 333314 sequences. (Running on oeis4.)