A079640 - OEIS

%I #15 Jun 26 2018 03:27:03

%S 1,3,1,14,9,1,88,83,18,1,694,860,275,30,1,6578,10084,4245,685,45,1,

%T 72792,132888,69244,14735,1435,63,1,920904,1950024,1209880,318969,

%U 41020,2674,84,1,13109088,31580472,22715972,7133784,1137549,98028,4578,108,1

%N Matrix product of unsigned Stirling1-triangle |A008275(n,k)| and unsigned Lah-triangle |A008297(n,k)|.

%C Also the Bell transform of A007840(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

%e 1; 3,1; 14,9,1; 88,83,18,1; 694,860,275,30,1; 6578,10084,4245,685,45,1; ...

%p # The function BellMatrix is defined in A264428.

%p # Adds (1, 0, 0, 0, ..) as column 0.

%p BellMatrix(n -> add(k!*abs(combinat:-stirling1(n+1, k)), k=0..n+1), 9); # _Peter Luschny_, Jan 26 2016

%t BellMatrix[f_Function, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];

%t rows = 12;

%t M = BellMatrix[Function[n, Sum[k!*Abs[StirlingS1[n+1, k]], {k, 0, n+1}]], rows];

%t Table[M[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* _Jean-François Alcover_, Jun 26 2018, after _Peter Luschny_ *)

%Y Cf. A007840 (first column).

%K nonn,tabl

%O 1,2

%A _Vladeta Jovovic_, Jan 30 2003