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A088814 Matrix product of unsigned Lah-triangle |A008297(n,k)| and Stirling2-triangle A008277(n,k).

%I A088814 #9 Jun 28 2018 02:43:30
%S A088814 1,3,1,13,9,1,73,79,18,1,501,755,265,30,1,4051,7981,3840,665,45,1,
%T A088814 37633,93135,57631,13580,1400,63,1,394353,1192591,911582,274141,38290,
%U A088814 2618,84,1,4596553,16645431,15285313,5633922,999831,92358,4494,108,1,58941091
%N A088814 Matrix product of unsigned Lah-triangle |A008297(n,k)| and Stirling2-triangle A008277(n,k).
%C A088814 Also the Bell transform of A000262(n+1). For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 26 2016
%F A088814 E.g.f.: exp(y*(exp(x/(1-x))-1)).
%p A088814 # The function BellMatrix is defined in A264428.
%p A088814 # Adds (1, 0, 0, 0, ..) as column 0.
%p A088814 BellMatrix(n -> simplify(hypergeom([-n,-n-1],[],1)), 9); # _Peter Luschny_, Jan 26 2016
%t A088814 BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
%t A088814 rows = 12;
%t A088814 B = BellMatrix[Function[n, Sum[BellY[n+1, k, Range[n+1]!], {k, 0, n+1}]], rows];
%t A088814 Table[B[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* _Jean-François Alcover_, Jun 28 2018, after Peter Luschny_ *)
%Y A088814 Cf. A000262(first column), A084357(row sums).
%K A088814 nonn,tabl
%O A088814 1,2
%A A088814 _Vladeta Jovovic_, Nov 22 2003