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Search: id:A008550
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| A008550 |
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Table T(n,k), n>=0 and k>=0, read by antidiagonals: the k-th column given by the k-th Narayana polynomial. |
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3
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| 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 3, 1, 1, 1, 14, 11, 4, 1, 1, 1, 42, 45, 19, 5, 1, 1, 1, 132, 197, 100, 29, 6, 1, 1, 1, 429, 903, 562, 185, 41, 7, 1, 1, 1, 1430, 4279, 3304, 1257, 306, 55, 8, 1, 1, 1, 4862, 20793, 20071, 8925, 2426, 469, 71, 9, 1, 1
(list; table; graph; listen)
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OFFSET
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0,8
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LINKS
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H. Prodinger, On a functional difference equation...
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FORMULA
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T(n, k) = Sum_{j>0} A001263(k, j)*n^(j-1); T(n, 0)=1.
T(n, k) = Sum_{j, 0<=j<=k} A088617(k, j)*n^j*(1-n)^(k-j).
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EXAMPLE
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Row n=0: 1, 1, 1, 1, 1, 1, 1, 1, ... see A000012.
Row n=1: 1, 1, 2, 5, 14, 42, 132, 429, ... see A000108.
Row n=2: 1, 1, 3, 11, 45, 197, 903, 4279, ...see A001003.
Row n=3: 1, 1, 4, 19, 100, 562, 3304, 20071, ...see A007564.
Row n=4: 1, 1, 5, 29, 185, 1257, 8925, ...see A005923.
Row n=5: 1, 1, 6, 41, 306, 2426, 20076, ...see A078009.
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CROSSREFS
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Other rows: A078018, A081178, A082147, A082181, A081148, A082173.
Columns: A000012, A000012, A000027, A028387, A090197, A090198, A090199, A090200.
Main diagonal is in A099169.
Sequence in context: A155586 A069739 A066060 this_sequence A064094 A090182 A111673
Adjacent sequences: A008547 A008548 A008549 this_sequence A008551 A008552 A008553
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Jan 23 2004
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