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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

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

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

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Last modified December 2 05:01 EST 2021. Contains 349437 sequences. (Running on oeis4.)