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Triangle read by rows, related to A108283.
3

%I #8 Sep 13 2016 11:54:20

%S 1,3,2,6,11,6,10,39,54,24,15,114,304,324,120,21,300,1384,2664,2280,

%T 720,28,741,5598,17364,25800,18360,5040,36,1757,21054,99012,227400,

%U 273720,166320,40320,45,4052,75504,518592,1728816,3131400,3160080,1673280,362880,55,9162,262104,2564892,11934816,30523800,45496080,39473280,18506880,3628800

%N Triangle read by rows, related to A108283.

%F n-th row is the inverse binomial transform of n-th column of A108283.

%e Triangle begins:

%e 1;

%e 3, 2;

%e 6, 11, 6;

%e 10, 39, 54, 24;

%e 15, 114, 304, 324, 120; ...

%e Row 2: (3, 2, 0, 0, 0...), is the inverse binomial transform of column 2 of A108283: (3, 5, 7, 9...).

%t (* T = A108283 *) T[_, 1] := 1; T[n_, n_] := n*(n + 1)/2; T[n_, k_] := (1 - (n - k + 1)^k*(k^2 - k*n + 1))/(n - k)^2; row[n_] := (TT = Table[T[k, n], {k, n, 2*n - 1}]; Table[Differences[TT, k], {k, 0, n - 1}][[All, 1]]); Table[row[n], {n, 1, 10}] // Flatten (* _Jean-François Alcover_, Sep 13 2016 *)

%Y Cf. A108283.

%K nonn,tabl

%O 1,2

%A _Gary W. Adamson_, May 30 2005

%E More terms from _Jean-François Alcover_, Sep 13 2016