

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
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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 nth 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^(nj)])(b(nj)*
binomial(n1, j1)), 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 (* JeanFrançois Alcover, Jun 12 2018, after Alois P. Heinz *)


CROSSREFS

Cf. A000110, A186020.
Sequence in context: A124218 A025165 A345278 * A346517 A318354 A348373
Adjacent sequences: A212428 A212429 A212430 * A212432 A212433 A212434


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Jun 21 2012


EXTENSIONS

Edited by N. J. A. Sloane, Jun 22 2012


STATUS

approved



