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A288778 Triangle read by rows (1<=k<=n): T(n,k) = (n-k+1)*k! - (k-1)! 2
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, 1320, 4320, 7, 13, 34, 114, 456, 2040, 9360, 35280, 8, 15, 40, 138, 576, 2760, 14400, 75600, 322560, 9, 17, 46, 162, 696, 3480, 19440, 115920, 685440, 3265920, 10, 19, 52, 186, 816, 4200, 24480, 156240, 1048320, 6894720, 36288000 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..66.

FORMULA

T(n,k) = A288777(n,k) - A000142(k-1), n>=1.

EXAMPLE

Triangle begins:

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, 1320,  4320;

7,  13, 34, 114, 456, 2040,  9360,  35280;

8,  15, 40, 138, 576, 2760, 14400,  75600,  322560;

9,  17, 46, 162, 696, 3480, 19440, 115920,  685440, 3265920;

10, 19, 52, 186, 816, 4200, 24480, 156240, 1048320, 6894720, 36288000;

...

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).

MATHEMATICA

Table[(n - k + 1) k! - (k - 1)!, {n, 11}, {k, n}] // Flatten (* Michael De Vlieger, Jun 16 2017 *)

CROSSREFS

Column 1 gives A001477.

Row sums give A288780.

Cf. A000142, A004736, A166350, A215014, A288777.

Sequence in context: A078908 A159797 A152920 * A290139 A317588 A080383

Adjacent sequences:  A288775 A288776 A288777 * A288779 A288780 A288781

KEYWORD

nonn,tabl,easy

AUTHOR

Omar E. Pol, Jun 15 2017

STATUS

approved

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Last modified May 20 12:33 EDT 2019. Contains 323422 sequences. (Running on oeis4.)