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A189233
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Square array A(n,k), n >= 0, k >= 0, read by diagonals, where the e.g.f. of column k is exp(k*(e^x-1)).
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8
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1, 0, 1, 0, 1, 1, 0, 2, 2, 1, 0, 5, 6, 3, 1, 0, 15, 22, 12, 4, 1, 0, 52, 94, 57, 20, 5, 1, 0, 203, 454, 309, 116, 30, 6, 1, 0, 877, 2430, 1866, 756, 205, 42, 7, 1, 0, 4140, 14214, 12351, 5428, 1555, 330, 56, 8, 1
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OFFSET
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0,8
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COMMENTS
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A(n, 1) = A000110(n), A(n, -1) = A000587(n).
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REFERENCES
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E. T. Bell, Exponential numbers, Amer. Math. Monthly, 41 (1934), 411-419.
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LINKS
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Table of n, a(n) for n=0..54.
Peter Luschny, Set partitions and Bell numbers
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FORMULA
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E.g.f. of column k is exp(k*(e^x-1)).
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EXAMPLE
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Square array begins:
A000007 A000110 A001861 A027710 A078944 A144180 A144223 A144263
A000012 1, 1, 1, 1, 1, 1, 1, 1, ...
A001477 0, 1, 2, 3, 4, 5, 6, 7, ...
A002378 0, 2, 6, 12, 20, 30, 42, 56, ...
A033445 0, 5, 22, 57, 116, 205, 330, 497, ...
0, 15, 94, 309, 756, 1555, 2850, 4809, ...
0, 52, 454, 1866, 5428, 12880, 26682, 50134, ...
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MAPLE
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# Cf. also the Maple prog. of Alois P. Heinz in A144223 and A144180.
expnums := proc(k, n) option remember; local j;
`if`(n = 0, 1, (1+add(binomial(n-1, j-1)*expnums(k, n-j), j = 1..n-1))*k) end:
A189233_array := (k, n) -> expnums(k, n):
seq(print(seq(A189233_array(k, n), k = 0..7)), n = 0..5);
A189233_egf := k -> exp(k*(exp(x)-1));
T := (n, k) -> n!*coeff(series(A189233_egf(k), x, n+1), x, n):
seq(lprint(seq(T(n, k), k = 0..7)), n = 0..5):
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CROSSREFS
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Cf. A144150.
Sequence in context: A120059 A067347 A120568 * A065066 A064045 A110314
Adjacent sequences: A189230 A189231 A189232 * A189234 A189235 A189236
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KEYWORD
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nonn,tabl
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AUTHOR
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Peter Luschny, Apr 18 2011
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STATUS
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approved
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