cp's OEIS Frontend

A079642 Matrix product of unsigned Stirling1-triangle |A008275(n,k)| and Stirling1-triangle A008275(n,k).

%I A079642 #14 Jun 28 2018 08:24:49
%S A079642 1,0,1,1,0,1,1,4,0,1,8,5,10,0,1,26,58,15,20,0,1,194,217,238,35,35,0,1,
%T A079642 1142,2035,1008,728,70,56,0,1,9736,13470,11611,3444,1848,126,84,0,1,
%U A079642 81384,134164,85410,47815,9660,4116,210,120,0,1,823392,1243770,983059
%N A079642 Matrix product of unsigned Stirling1-triangle |A008275(n,k)| and Stirling1-triangle A008275(n,k).
%C A079642 Also the Bell transform of A089064(n+1). For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 26 2016
%F A079642 T(n, k) = Sum_{i=k..n} |A008275(n, i)| * A008275(i, k).
%F A079642 E.g.f.: (1-log(1-x))^y. - _Vladeta Jovovic_, Nov 22 2003
%e A079642 1; 0,1; 1,0,1; 1,4,0,1; 8,5,10,0,1; 26,58,15,20,0,1; ...
%p A079642 # The function BellMatrix is defined in A264428.
%p A079642 # Adds (1, 0, 0, 0, ..) as column 0.
%p A079642 BellMatrix(n -> add((-1)^n*(k-1)!*combinat:-stirling1(n+1, k), k=1..n+1), 9); # _Peter Luschny_, Jan 26 2016
%t A079642 BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
%t A079642 B = BellMatrix[Function[n, Sum[(-1)^n*(k-1)! StirlingS1[n+1, k], {k, 1, n+1} ] ], rows = 12];
%t A079642 Table[B[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* _Jean-François Alcover_, Jun 28 2018, after _Peter Luschny_ *)
%K A079642 nonn,tabl
%O A079642 1,8
%A A079642 _Vladeta Jovovic_, Jan 30 2003