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Triangle, A000110 in every column > 0, shifted down twice.
3

%I #11 Nov 19 2022 15:55:38

%S 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,

%T 21147,877,52,5,1,115975,4140,203,15,2,1,678570,21147,877,52,5,1,

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

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

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

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

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

%e First few rows of the triangle:

%e 1;

%e 1;

%e 2, 1;

%e 5, 1;

%e 15, 2, 1;

%e 52, 5, 1;

%e 203, 15, 2, 1;

%e 877, 52, 5, 1;

%e 4140, 203, 15, 2, 1;

%e 21147, 877, 52, 5, 1;

%e 115975, 4140, 203, 15, 2, 1;

%e ...

%t T[n_, k_] := BellB[n - 2 k];

%t Table[T[n, k], {n, 0, 10}, {k, 0, Quotient[n, 2]}] // Flatten (* _Jean-François Alcover_, Apr 22 2022 *)

%o (PARI) B(n) = sum(k=0, n, stirling(n, k, 2)); \\ A000110

%o tabf(nn) = for (n=0, nn, for(k=0, n\2, print1(B(n-2*k), ", "));); \\ _Michel Marcus_, Nov 19 2022

%Y Cf. A000110, A173109, A173110, A173111.

%K nonn,tabf

%O 0,3

%A _Gary W. Adamson_, Feb 09 2010

%E Keyword tabf and more terms from _Michel Marcus_, Nov 19 2022