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Search: id:A126350
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| A126350 |
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Triangle read by rows: matrix product of the binomial coefficients with the Stirling numbers of the second kind. |
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4
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| 1, 1, 2, 1, 5, 5, 1, 9, 22, 15, 1, 14, 61, 99, 52, 1, 20, 135, 385, 471, 203, 1, 27, 260, 1140, 2416, 2386, 877, 1, 35, 455, 2835, 9156, 15470, 12867, 4140, 1, 44, 742, 6230, 28441, 72590, 102215, 73681, 21147
(list; table; graph; listen)
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OFFSET
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1,3
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COMMENT
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Many well-known integer sequences arise from such a matrix product of combinatorial coefficients. In the present case we have as the first row (not surprisingly) A000110 = Bell or exponential numbers: ways of placing n labeled balls into n indistinguishable boxes . As second row we have A033452 = "STIRLING" transform of squares A000290. As the column sums we have 1, 3, 11, 47, 227, 1215, 7107, 44959, 305091 which is A035009 = STIRLING transform of [1,1,2,4,8,16,32, ...].
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LINKS
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Thomas Wieder, Home Page.
Thomas Wieder, (Old) Home Page.
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FORMULA
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(In Maple notation:) Matrix product A.B of matrix A[i,j]:=binomial(j-1,i-1) with i = 1 to p+1, j = 1 to p+1, p=8 and of matrix B[i,j]:=stirling2(j,i) with i from 1 to d, j from 1 to d, d=9.
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EXAMPLE
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Matrix begins:
1 2 5 15 52 203 877 4140 21147
0 1 5 22 99 471 2386 12867 73681
0 0 1 9 61 385 2416 15470 102215
0 0 0 1 14 135 1140 9156 72590
0 0 0 0 1 20 260 2835 28441
0 0 0 0 0 1 27 455 6230
0 0 0 0 0 0 1 35 742
0 0 0 0 0 0 0 1 44
0 0 0 0 0 0 0 0 1
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CROSSREFS
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Cf. A039810, A039814, A126351, A054654, A126353.
Sequence in context: A111785 A021468 A033282 this_sequence A079502 A126124 A060920
Adjacent sequences: A126347 A126348 A126349 this_sequence A126351 A126352 A126353
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KEYWORD
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nonn,tabl
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AUTHOR
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Thomas Wieder (thomas.wieder(AT)t-online.de), Dec 29 2006
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