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%I #26 Jun 20 2017 23:35:05
%S 0,1,1,2,3,4,3,5,10,18,4,7,16,42,96,5,9,22,66,216,600,6,11,28,90,336,
%T 1320,4320,7,13,34,114,456,2040,9360,35280,8,15,40,138,576,2760,14400,
%U 75600,322560,9,17,46,162,696,3480,19440,115920,685440,3265920,10,19,52,186,816,4200,24480,156240,1048320,6894720,36288000
%N Triangle read by rows (1<=k<=n): T(n,k) = (n-k+1)*k! - (k-1)!
%C T(10,k) is also the number of positive integers with k digits in the sequence A215014. See _Franklin T. Adams-Watters_'s comment in that entry. See also A288780.
%F T(n,k) = A288777(n,k) - A000142(k-1), n>=1.
%e Triangle begins:
%e 0;
%e 1, 1;
%e 2, 3, 4;
%e 3, 5, 10, 18;
%e 4, 7, 16, 42, 96;
%e 5, 9, 22, 66, 216, 600;
%e 6, 11, 28, 90, 336, 1320, 4320;
%e 7, 13, 34, 114, 456, 2040, 9360, 35280;
%e 8, 15, 40, 138, 576, 2760, 14400, 75600, 322560;
%e 9, 17, 46, 162, 696, 3480, 19440, 115920, 685440, 3265920;
%e 10, 19, 52, 186, 816, 4200, 24480, 156240, 1048320, 6894720, 36288000;
%e ...
%e For n = 10 and k = 2; T(10,2) = 17 coincides with the number of positive terms with two digits in A215014 (see the first comment above).
%t Table[(n - k + 1) k! - (k - 1)!, {n, 11}, {k, n}] // Flatten (* _Michael De Vlieger_, Jun 16 2017 *)
%Y Column 1 gives A001477.
%Y Row sums give A288780.
%Y Cf. A000142, A004736, A166350, A215014, A288777.
%K nonn,tabl,easy
%O 1,4
%A _Omar E. Pol_, Jun 15 2017
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