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
Alois P. Heinz, Rows n = 0..140, flattened
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
KEYWORD
nonn,tabl
AUTHOR
Gary W. Adamson, Jun 21 2012
EXTENSIONS
Edited by N. J. A. Sloane, Jun 22 2012
STATUS
approved