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A212431
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Triangle read by rows: row sums, right and left borders are the Bell sequence, or a shifted variant. See Comments for precise definition.
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2
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1, 1, 1, 2, 1, 2, 5, 3, 2, 5, 15, 9, 8, 5, 15, 52, 31, 28, 25, 15, 52, 203, 121, 108, 100, 90, 52, 203, 877, 523, 466, 425, 405, 364, 203, 877, 4140, 2469, 2202, 2000, 1875, 1820, 1624, 877, 4140, 21147, 12611, 11250, 10230, 9525, 9100, 8932, 7893, 4140, 21147
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OFFSET
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0,4
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COMMENTS
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Consider A186020 as an infinite lower triangular matrix, and multiply the columns successively by the Bell numbers A000110, (1, 1, 2, 5, 15, 52,...).
Right and left borders = the Bell numbers, A000110: (1, 1, 2, 5, 15,...). Row sums = the shifted Bell numbers, (1, 2, 5, 15, 52,...).
Sum of n-th row terms = rightmost and leftmost terms of next row.
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LINKS
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1
2, 1, 2;
5, 3, 2, 5;
15, 9, 8, 5, 15;
52, 31, 28, 25, 15, 52;
203, 121, 108, 100, 90, 52, 203;
877, 523, 466, 425, 405, 364, 203, 877;
4140, 2469, 2202, 2000, 1875, 1820, 1624, 877, 4140;
21147, 12611, 11250, 10230, 9525, 9100, 8932, 7893, 4140, 21147;
...
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MAPLE
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b:= proc(n) option remember; `if`(n=0, [1, 0],
add((p-> p+[0, p[1]*x^(n-j)])(b(n-j)*
binomial(n-1, j-1)), j=1..n))
end:
T:= n-> (p-> seq(`if`(i=n, p[1], coeff(
p[2], x, i)), i=0..n))(b(n)):
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MATHEMATICA
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b[n_] := b[n] = If[n == 0, {1, 0}, Sum[Function[p, p + {0, p[[1]]*x^(n - j)}][b[n - j]*Binomial[n - 1, j - 1]], {j, 1, n}]];
T[n_] := Function[p, Table[If[i == n, p[[1]], Coefficient[p[[2]], x, i]], {i, 0, n}]][b[n]];
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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