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Search: id:A126351
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| A126351 |
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Triangle read by rows: matrix product of the Stirling numbers of the second kind with the binomial coefficients. |
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5
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| 1, 1, 2, 1, 5, 4, 1, 9, 19, 8, 1, 14, 55, 65, 16, 1, 20, 125, 285, 211, 32, 1, 27, 245, 910, 1351, 665, 64, 1, 35, 434, 2380, 5901, 6069, 2059, 128, 1, 44, 714, 5418, 20181, 35574, 26335, 6305, 256
(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 A000079 = the powers of two = 2^n . As the second row we have A001047 = 3^n - 2^n. As the column sums we have 1,3,10,37,151,674,3263,17007,94828 we have A005493 = number of partitions of [n+1] with a distinguished block.
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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 B.A 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 4 8 16 32 64 128 256,
0 1 5 19 65 211 665 2059 6305
0 0 1 9 55 285 1351 6069 26335
0 0 0 1 14 125 910 5901 35574
0 0 0 0 1 20 245 2380 20181
0 0 0 0 0 1 27 434 5418
0 0 0 0 0 0 1 35 714
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, A126350, A054654, A126353.
Sequence in context: A056242 A128718 A112358 this_sequence A157011 A092821 A110552
Adjacent sequences: A126348 A126349 A126350 this_sequence A126352 A126353 A126354
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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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