A173108 Triangle, A000110 in every column > 0, shifted down twice.

1, 1, 2, 1, 5, 1, 15, 2, 1, 52, 5, 1, 203, 15, 2, 1, 877, 52, 5, 1, 4140, 203, 15, 2, 1, 21147, 877, 52, 5, 1, 115975, 4140, 203, 15, 2, 1, 678570, 21147, 877, 52, 5, 1, 4213597, 115975, 4140, 203, 15, 2, 1, 27644437, 678570, 21147, 877, 52, 5, 1

Offset: 0

Author

Gary W. Adamson, Feb 09 2010

Keywords

• nonn
• tabf

Comments

Row sums = A173109: (1, 1, 3, 6, 18, 58, 221, 935, ...).

Let the triangle = M. Then lim_{n->oo} M^n = A173110: (1, 1, 3, 6, 20, 60, ...).

Examples

			First few rows of the triangle:
       1;
       1;
       2,    1;
       5,    1;
      15,    2,   1;
      52,    5,   1;
     203,   15,   2,  1;
     877,   52,   5,  1;
    4140,  203,  15,  2, 1;
   21147,  877,  52,  5, 1;
  115975, 4140, 203, 15, 2, 1;
  ...
		

Crossrefs

Cf. A000110, A173109, A173110, A173111.

Programs

Mathematica

T[n_, k_] := BellB[n - 2 k];
Table[T[n, k], {n, 0, 10}, {k, 0, Quotient[n, 2]}] // Flatten (* Jean-François Alcover, Apr 22 2022 *)

PARI

B(n) = sum(k=0, n, stirling(n, k, 2)); \\ A000110
tabf(nn) = for (n=0, nn, for(k=0, n\2, print1(B(n-2*k), ", "));); \\ Michel Marcus, Nov 19 2022

Formula

Bell sequence in every column, for columns > 0, shifted down twice.

Extensions

Keyword tabf and more terms from Michel Marcus, Nov 19 2022