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A212431 Triangle read by rows: row sums, right and left borders are the Bell sequence, or a shifted variant. See Comments for precise definition. 2
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
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.
LINKS
EXAMPLE
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;
...
MAPLE
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)):
seq(T(n), n=0..12); # Alois P. Heinz, May 16 2017
MATHEMATICA
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]];
Table[T[n], {n, 0, 12}] // Flatten (* Jean-François Alcover, Jun 12 2018, after Alois P. Heinz *)
CROSSREFS
Sequence in context: A124218 A025165 A345278 * A346517 A318354 A348373
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 21 2012
EXTENSIONS
Edited by N. J. A. Sloane, Jun 22 2012
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)