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Search: id:A143632
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| A143632 |
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Table T(n,k), n>=0, k>=0, read by antidiagonals, where the e.g.f. for column k satisfies A_k(x) = exp(x*A_k(((x+1)^k-1)/k)) if k>0 and A_0(x) = exp(x*A_0(0)) = exp(x). |
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9
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| 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 16, 1, 1, 1, 3, 19, 125, 1, 1, 1, 3, 22, 185, 1296, 1, 1, 1, 3, 25, 253, 2541, 16807, 1, 1, 1, 3, 28, 329, 4256, 45787, 262144, 1, 1, 1, 3, 31, 413, 6471, 96727, 1037359, 4782969, 1, 1, 1, 3, 34, 505, 9216, 175747, 2828274, 28649553
(list; table; graph; listen)
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OFFSET
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0,9
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EXAMPLE
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Table begins:
1, 1, 1, 1, 1, 1
1, 1, 1, 1, 1, 1
1, 3, 3, 3, 3, 3
1, 16, 19, 22, 25, 28
1, 125, 185, 253, 329, 413
1, 1296, 2541, 4256, 6471, 9216
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MAPLE
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A:= proc(n, k::nonnegint) option remember; if n<=0 or k=0 then 1 else A(n-1, k)(((x+1)^k-1)/k) fi; unapply (convert (series (exp (x*%), x, n+1), polynom), x) end: T:= (n, k)-> coeff (A(n, k)(x), x, n)*n!: seq (seq(T(n, d-n), n=0..d), d=0..11);
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CROSSREFS
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Cf. columns 0-9: A000012, A000272, A143633, A143634, A143635, A143636, A143637, A143638, A143639, A143640.
Sequence in context: A016466 A055210 A082553 this_sequence A130605 A157261 A079110
Adjacent sequences: A143629 A143630 A143631 this_sequence A143633 A143634 A143635
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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 27 2008
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