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Search: id:A158823
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| 1, 3, 1, 6, 2, 2, 10, 3, 4, 3, 15, 4, 6, 6, 4, 21, 5, 8, 9, 8, 5, 28, 6, 10, 12, 12, 10, 6, 36, 7, 12, 15, 16, 15, 12, 7, 45, 8, 14, 18, 20, 20, 18, 14, 8, 55, 9, 16, 21, 24, 25, 24, 21, 16, 9, 66, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10, 78, 11, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11, 91
(list; table; graph; listen)
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OFFSET
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1,2
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FORMULA
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sum_{m=1..n} T(n,m) = A000292(n).
T(n,m) = sum_{k=m..n} A004736(n,k)*A158821(k-1,m-1).
T(n,m) = A003991(n-1,m-1), m>1. [R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 22 2009, Oct 30 2009]
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EXAMPLE
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First few rows of the triangle =
1;
3, 1;
6, 2, 2;
10, 3, 4, 3;
15, 4, 6, 6, 4;
21, 5, 8, 9, 8, 5;
28, 6, 10, 12, 12, 10, 6;
36, 7, 12, 15, 16, 15, 12, 7;
45, 8, 14, 18, 20, 20, 18, 14, 8;
55, 9, 16, 21, 24, 25, 24, 21, 16, 9;
66, 10, 18, 24, 28, 30, 30, 28, 24, 18, 10;
78, 11, 20, 27, 32, 35, 36, 35, 32, 27, 20, 11;
91, 12, 22, 30, 36, 40, 42, 42, 40, 36, 30, 22, 12;
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MAPLE
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A004736 := proc(n, m) n-m+1 ; end:
A158821 := proc(n, m) if m = 0 then 1; elif m = n then n; else 0; fi; end:
A158823 := proc(n, m) add( A004736(n, k)*A158821(k-1, m-1), k=1..n) ; end: seq(seq(A158823(n, m), m=1..n), n=1..8) ;
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CROSSREFS
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Cf. A158821, A000292
Sequence in context: A055151 A104573 A010467 this_sequence A122913 A069115 A065275
Adjacent sequences: A158820 A158821 A158822 this_sequence A158824 A158825 A158826
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KEYWORD
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nonn,tabl,easy
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AUTHOR
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Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Mar 28 2009
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EXTENSIONS
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Maple program added by R. J. Mathar, (mathar(AT)strw.leidenuniv.nl), Oct 22 2009
Corrected A-number in a formula - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 30 2009
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