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Triangle read by rows: (2 * A011971) - A000012.
1

%I #12 Apr 02 2022 10:41:09

%S 1,1,3,3,5,9,9,13,19,29,29,39,53,73,103,103,133,173,227,301,405,405,

%T 509,643,817,1045,1347,1753,1753,2159,2669,3313,4131,5177,6525,8279,

%U 8279,100033,12193,14863,18177,22309,27487,34013,42293,42293,50573,60607,72801,87665,105843,128153,155641,189655,231949

%N Triangle read by rows: (2 * A011971) - A000012.

%C Right border = A060719: (1, 3, 9, 29, 103, ...).

%C Row sums = A136792.

%F (2 * A011971) - A000012, where A011971 = Aitken's triangle. Given Aitken's triangle, add 1 immediately after every addition operation. Rightmost term in (n-1)-th row becomes leftmost term in n-th row.

%e First few rows of the triangle:

%e 1;

%e 1, 3;

%e 3, 5, 9;

%e 9, 13, 19, 29;

%e 29, 39, 53, 73, 103;

%e 103, 133, 173, 227, 301, 405;

%e ...

%t Flatten[Table[2 Sum[Binomial[k, i]*BellB[n - k + i], {i, 0, k}] - 1, {n, 0, 9}, {k, 0, n}]] (* _Michael De Vlieger_, Apr 02 2022, after _Jean-François Alcover_ at A011971 *)

%Y Cf. A011971, A136792, A060719.

%K nonn,tabl

%O 0,3

%A _Gary W. Adamson_, Jan 21 2008