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%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
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