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%I #14 Jun 27 2018 02:47:08
%S 1,1,1,2,3,1,4,11,6,1,14,40,35,10,1,38,184,195,85,15,1,216,840,1204,
%T 665,175,21,1,600,4920,7616,5369,1820,322,28,1,6240,26616,54116,44016,
%U 18669,4284,546,36,1,9552,197856,392460,383480,191205,54453,9030,870,45,1,319296,1177176,3229776,3449600,2017070,679371,139293,17490,1320,55,1,-519312
%N Matrix product of Stirling1-triangle A008275(n,k) and unsigned Lah-triangle |A008297(n,k)|.
%C Also the Bell transform of A006252(n+1). For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 26 2016
%F T(n, k) = Sum_{i=k..n} A008275(n, i) * |A008297(i, k)|.
%F E.g.f: (1+x)^(y/(1-log(1+x))). - _Vladeta Jovovic_, Nov 22 2003
%p # The function BellMatrix is defined in A264428.
%p # Adds (1, 0, 0, 0, ..) as column 0.
%p BellMatrix(n -> add(k!*combinat:-stirling1(n+1,k),k=0..n+1),9); # _Peter Luschny_, Jan 26 2016
%t BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
%t rows = 12;
%t B = BellMatrix[Function[n, Sum[k!*StirlingS1[n+1, k], {k, 0, n+1}]], rows];
%t Table[B[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* _Jean-François Alcover_, Jun 27 2018, after _Peter Luschny_ *)
%Y Cf. A006252 (first column).
%K sign,tabl
%O 1,4
%A _Vladeta Jovovic_, Jan 30 2003
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