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Search: id:A123097
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| A123097 |
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Triangle read by rows: T(n,k)=binom(n-2,k-1)+n*binom(n-1,k-1), 1<=k<=n. |
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+0
1
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| 1, 3, 2, 4, 7, 3, 5, 14, 13, 4, 6, 23, 33, 21, 5, 7, 34, 66, 64, 31, 6, 8, 47, 115, 150, 110, 43, 7, 9, 62, 183, 300, 295, 174, 57, 8, 10, 79, 273, 539, 665, 525, 259, 73, 9, 11, 98, 388, 896, 1330, 1316, 868, 368, 91, 10, 12, 119, 531, 1404, 2436, 2898, 2394, 1356, 504
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Triangle is M*P, where M is the infinite bidiagonal matrix with (1,2,3...) in the main diagonal and (1,1,1...) in the subdiagonal and P is Pascal's triangle as an infinite lower triangular matrix. The triangle A124727=P*M.
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EXAMPLE
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First few rows of the triangle are:
1;
3, 2;
4, 7, 3;
5, 14, 13, 4
6, 23, 33, 21, 5;
7, 34, 66, 64, 31, 6;
...
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MAPLE
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T:=proc(n, k) if n=1 and k=1 then 1 elif n=1 then 0 else binomial(n-2, k-1)+n*binomial(n-1, k-1) fi end: for n from 1 to 12 do seq(T(n, k), k=1..n) od; # yields sequence in triangular form
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CROSSREFS
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Row sums = A052951: (1, 5, 14, 36, 88, 208...)
Sequence in context: A085346 A121861 A060006 this_sequence A134571 A054086 A163329
Adjacent sequences: A123094 A123095 A123096 this_sequence A123098 A123099 A123100
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Nov 05 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 24 2006
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