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

0,3

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, ...).

Links

Table of n, a(n) for n=0..55.

Formula

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

Example

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;
  ...

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 *)

Prog

(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

Crossrefs

Cf. A000110, A173109, A173110, A173111.

Sequence in context: A348497 A299161 A327249 * A173111 A363739 A257459

Adjacent sequences: A173105 A173106 A173107 * A173109 A173110 A173111

Keyword

nonn,tabf

Author

Gary W. Adamson, Feb 09 2010

Extensions

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

Status

approved