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Search: id:A125178
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| A125178 |
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Triangle read by rows: T(n,0)=B(n) (the Bell numbers, A000110(n)), T(n,k)=0 for k<0 or k>n, T(n,k)=T(n-1,k)+T(n-1,k-1) for n>=1, 0<=k<=n. |
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+0
2
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| 1, 1, 1, 2, 2, 1, 5, 4, 3, 1, 15, 9, 7, 4, 1, 52, 24, 16, 11, 5, 1, 203, 76, 40, 27, 16, 6, 1, 877, 279, 116, 67, 43, 22, 7, 1, 4140, 1156, 395, 183, 110, 65, 29, 8, 1, 21147, 5296, 1551, 578, 293, 175, 94, 37, 9, 1, 115975, 26443, 6847, 2129, 871, 468, 269, 131, 46, 10, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Row sums = 1, 2, 5, 13, 36, 109, 369,...
Columns 0,1 and 2 yield A000110,A005001 and A029761, respectively.
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
2, 2, 1;
5, 4, 3, 1;
15, 9, 7, 4, 1;
52, 24, 16, 11, 5, 1;
203, 76, 40, 27, 16, 6, 1;
...
(4,3) = 16 = 7 + 9 = (3,3) + (3,2).
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MAPLE
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with(combinat): T:=proc(n, k) if k=0 then bell(n) elif k<0 or k>n then 0 else T(n-1, k)+T(n-1, k-1) fi end: for n from 0 to 11 do seq(T(n, k), k=0..n) od; # yields sequence in triangular form
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CROSSREFS
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Cf. A000110, A005001, A029761.
Sequence in context: A121460 A105292 A125177 this_sequence A101975 A136388 A099605
Adjacent sequences: A125175 A125176 A125177 this_sequence A125179 A125180 A125181
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 22 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 29 2006
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