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Square table, read by antidiagonals, of coefficients T(k,n) (row k; column n) defined by :T(k,n) = k*T(k,n-1)+ n; T(k,0) = 0.
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%I #8 Feb 22 2013 14:38:50

%S 0,1,0,2,1,0,3,3,1,0,4,6,4,1,0,5,10,11,5,1,0,6,15,26,18,6,1,0,7,21,57,

%T 58,27,7,1,0,8,28,120,179,112,38,8,1,0,9,36,247,543,453,194,51,9,1,0,

%U 10,45,502,1636,1818,975,310,66,10,1,0

%N Square table, read by antidiagonals, of coefficients T(k,n) (row k; column n) defined by :T(k,n) = k*T(k,n-1)+ n; T(k,0) = 0.

%F T(k, n)= (k^(n+1)- (k-1)*n - k)/(k-1)^2. T(k, n) = Sum(j, 0<=j<=n; j*k^(n-j)).

%Y Rows begin:

%Y {0, 1, 2, 3, 4, 5, 6, 7, 8, ...}:see A001477

%Y {0, 1, 3, 6, 10, 15, 21, 28, ...} : see A000217

%Y {0, 1, 4, 11, 26, 57, 120, 247, 502, ...} : see A000295

%Y {0, 1, 5, 18, 58, 179, 543, 1636, ...} : see A000340

%Y {0, 1, 6, 27, 112, 453, 1818, 7279, ...} : see A014825

%Y {0, 1, 7, 38, 194, 975, 4881, 24412, ...} : see A014827

%Y {0, 1, 8, 51, 310, 1865, 11196, 67183, ...}: see diagonals of triangle A088990

%Y Diagonal begin:

%Y {0, 1, 4, 18, 112, 975, 11196, ... } :see A062805

%Y {0, 1, 5, 27, 194, 1865, ...} : see A023811

%Y Column {3, 6, 11, 18, 27, 38, 51, ...} : see A010000

%K easy,nonn,tabl

%O 0,4

%A _Philippe Deléham_, Nov 02 2003