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Array T(n,k) = A153277(n-1,k) = A144150(n,k-1) read by downwards antidiagonals.
3

%I #18 Sep 02 2022 13:38:37

%S 1,1,1,1,2,1,1,3,5,1,1,4,12,15,1,1,5,22,60,52,1,1,6,35,154,358,203,1,

%T 1,7,51,315,1304,2471,877,1,1,8,70,561,3455,12915,19302,4140,1

%N Array T(n,k) = A153277(n-1,k) = A144150(n,k-1) read by downwards antidiagonals.

%C Column k is obtained by taking the k-th matrix power of the triangle A008277 and multiplying from the right with the column vector [1,0,0,0,....].

%H Gabriella Bretti, Pierpaolo Natalini and Paolo E. Ricci, <a href="https://doi.org/10.1515/gmj-2019-2007">A new set of Sheffer-Bell polynomials and logarithmic numbers</a>, Georgian Mathematical Journal, Feb. 2019, page 4.

%e The array starts

%e 1, 1, 1, 1, 1, 1, ...

%e 1, 2, 3, 4, 5, 6, ...

%e 1, 5, 12, 22, 35, 51, ...

%e 1, 15, 60, 154, 315, 561, ...

%e 1, 52, 358, 1304, 3455, 7556, ...

%Y Cf. A008277, A144150, A153277.

%Y Cf. A000326 (row 3), A005945 (row 4), A000110 (column 2), A000258 (column 3), A000307 (column 4), A000357 (column 5), A000405 (column 6), A111669 (column 7), A081624.

%K nonn,tabl

%O 1,5

%A _Gary W. Adamson_, Aug 14 2005

%E a(44) and definition corrected by _Georg Fischer_, May 18 2022