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A088814
Matrix product of unsigned Lah-triangle |A008297(n,k)| and Stirling2-triangle A008277(n,k).
2
1, 3, 1, 13, 9, 1, 73, 79, 18, 1, 501, 755, 265, 30, 1, 4051, 7981, 3840, 665, 45, 1, 37633, 93135, 57631, 13580, 1400, 63, 1, 394353, 1192591, 911582, 274141, 38290, 2618, 84, 1, 4596553, 16645431, 15285313, 5633922, 999831, 92358, 4494, 108, 1, 58941091
OFFSET
1,2
COMMENTS
Also the Bell transform of A000262(n+1). For the definition of the Bell transform see A264428. - Peter Luschny, Jan 26 2016
FORMULA
E.g.f.: exp(y*(exp(x/(1-x))-1)).
MAPLE
# The function BellMatrix is defined in A264428.
# Adds (1, 0, 0, 0, ..) as column 0.
BellMatrix(n -> simplify(hypergeom([-n, -n-1], [], 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}]];
rows = 12;
B = BellMatrix[Function[n, Sum[BellY[n+1, k, Range[n+1]!], {k, 0, n+1}]], rows];
Table[B[[n, k]], {n, 2, rows}, {k, 2, n}] // Flatten (* Jean-François Alcover, Jun 28 2018, after Peter Luschny_ *)
CROSSREFS
Cf. A000262(first column), A084357(row sums).
Sequence in context: A133176 A089435 A152474 * A088729 A270968 A142888
KEYWORD
nonn,tabl
AUTHOR
Vladeta Jovovic, Nov 22 2003
STATUS
approved