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A306245
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Square array A(n,k), n>=0, k>=0, read by antidiagonals, where A(0,k) = 1 and A(n,k) = Sum_{j=0..n-1} k^j * binomial(n-1,j) * A(j,k) for n > 0.
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2
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1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 5, 1, 1, 1, 4, 17, 15, 1, 1, 1, 5, 43, 179, 52, 1, 1, 1, 6, 89, 1279, 3489, 203, 1, 1, 1, 7, 161, 5949, 108472, 127459, 877, 1, 1, 1, 8, 265, 20591, 1546225, 26888677, 8873137, 4140, 1
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history;
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OFFSET
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0,9
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LINKS
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Seiichi Manyama, Antidiagonals n = 0..55, flattened
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EXAMPLE
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Square array begins:
1, 1, 1, 1, 1, 1, ...
1, 1, 1, 1, 1, 1, ...
1, 2, 3, 4, 5, 6, ...
1, 5, 17, 43, 89, 161, ...
1, 15, 179, 1279, 5949, 20591, ...
1, 52, 3489, 108472, 1546225, 12950796, ...
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MAPLE
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A:= proc(n, k) option remember; `if`(n=0, 1,
add(k^j*binomial(n-1, j)*A(j, k), j=0..n-1))
end:
seq(seq(A(n, d-n), n=0..d), d=0..12); # Alois P. Heinz, Jul 28 2019
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CROSSREFS
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Columns k=0..2 give A000012, A000110, A126443.
Rows n=0+1, 2 give A000012, A000027(n+1).
Main diagonal gives A309401.
Cf. A309386.
Sequence in context: A144150 A124560 A290759 * A275043 A227061 A201949
Adjacent sequences: A306242 A306243 A306244 * A306246 A306247 A306248
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KEYWORD
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nonn,tabl
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AUTHOR
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Seiichi Manyama, Jul 28 2019
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STATUS
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approved
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