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

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, 1142, 2035, 1008, 728, 70, 56, 0, 1, 9736, 13470, 11611, 3444, 1848, 126, 84, 0, 1, 81384, 134164, 85410, 47815, 9660, 4116, 210, 120, 0, 1, 823392, 1243770, 983059

Offset

1,8

Comments

Also the Bell transform of A089064(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 26 2016

Links

Table of n, a(n) for n=1..58.

Formula

T(n, k) = Sum_{i=k..n} |A008275(n, i)| * A008275(i, k).

E.g.f.: (1-log(1-x))^y. - Vladeta Jovovic, Nov 22 2003

Example

1; 0,1; 1,0,1; 1,4,0,1; 8,5,10,0,1; 26,58,15,20,0,1; ...

Maple

# The function BellMatrix is defined in A264428.
# Adds (1, 0, 0, 0, ..) as column 0.
BellMatrix(n -> add((-1)^n*(k-1)!*combinat:-stirling1(n+1, k), k=1..n+1), 9); # Peter Luschny, Jan 26 2016

Mathematica

BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
B = BellMatrix[Function[n, Sum[(-1)^n*(k-1)! StirlingS1[n+1, k], {k, 1, n+1} ] ], rows = 12];
Table[B[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* Jean-François Alcover, Jun 28 2018, after Peter Luschny *)

Crossrefs

Sequence in context: A255644 A355174 A059678 * A342911 A221483 A121408

Adjacent sequences: A079639 A079640 A079641 * A079643 A079644 A079645

Keyword

nonn,tabl

Author

Vladeta Jovovic, Jan 30 2003

Status

approved