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Search: id:A099020
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| A099020 |
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Euler-Seidel matrix T(k,n) with start sequence A001147, read by antidiagonals. |
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+0
4
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| 1, 1, 0, 2, 1, 1, 4, 2, 1, 0, 10, 6, 4, 3, 3, 26, 16, 10, 6, 3, 0, 76, 50, 34, 24, 18, 15, 15, 232, 156, 106, 72, 48, 30, 15, 0, 764, 532, 376, 270, 198, 150, 120, 105, 105, 2620, 1856, 1324, 948, 678, 480, 330, 210, 105, 0, 9496, 6876, 5020, 3696, 2748, 2070
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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In an Euler-Seidel matrix, the rows are consecutive pairwise sums and the columns consecutive differences, with the first column the inverse binomial transform of the start sequence.
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LINKS
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D. Dumont, Matrices d'Euler-Seidel, Sem. Loth. Comb. B05c (1981) 59-78.
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FORMULA
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Recurrence: T(0, 2n) = (2n-1)!!, T(0, 2n+1) = 0, T(k, n) = T(k-1, n) + T(k-1, n+1).
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EXAMPLE
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1,0,1,0,3,0,15,
1,1,1,3,3,15,15,
2,2,4,6,18,30,120,
4,6,10,24,48,150,330,
10,16,34,72,198,480,1590,
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CROSSREFS
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First column is A000085, main diagonal is in A099021.
Sequence in context: A125138 A021477 A124939 this_sequence A089688 A092479 A124022
Adjacent sequences: A099017 A099018 A099019 this_sequence A099021 A099022 A099023
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KEYWORD
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nonn,tabl
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AUTHOR
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Ralf Stephan, Sep 23 2004
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