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Search: id:A143565
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| A143565 |
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Triangle T(n,k), n>=1, 1<=k<=n, where the e.g.f. for column k satisfies: A_k(x) = exp(x*A_k(x^k/k!)). |
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9
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| 1, 3, 1, 16, 4, 1, 125, 13, 5, 1, 1296, 46, 21, 6, 1, 16807, 241, 61, 31, 7, 1, 262144, 1471, 211, 106, 43, 8, 1, 4782969, 9409, 1401, 281, 169, 57, 9, 1, 100000000, 67348, 8065, 946, 505, 253, 73, 10, 1, 2357947691, 564841, 37241, 7561, 1261, 841, 361, 91, 11, 1
(list; table; graph; listen)
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OFFSET
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0,2
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FORMULA
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E.g.f. for column k satisfies: A_k(x) = exp(x*A_k(x^k/k!)).
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EXAMPLE
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Triangle begins:
1
3, 1
16, 4, 1
125, 13, 5, 1
1296, 46, 21, 6, 1
16807, 241, 61, 31, 7, 1
262144, 1471, 211, 106, 43, 8, 1
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MAPLE
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A:= proc(n, k::posint) option remember; if n<=0 then 1 else unapply (convert (series (exp (x*A(n-k, k)(x^k/k!)), x, n+1), polynom), x) fi end: T:= (n, k)-> coeff (A(n, k)(x), x, n)*n!: seq (seq(T(n, k), k=1..n), n=1..12);
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CROSSREFS
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Columns 1-9: A000272, A143566, A143567, A143568, A143569, A143570, A143571, A143572, A143573.
Sequence in context: A089278 A087071 A053485 this_sequence A143018 A102012 A128249
Adjacent sequences: A143562 A143563 A143564 this_sequence A143566 A143567 A143568
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KEYWORD
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nonn,tabl
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AUTHOR
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Alois P. Heinz (heinz(AT)hs-heilbronn.de), Aug 24 2008
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