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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.)