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A126885 T(n,k) = n*T(n,k-1) + k, with T(n,1) = 1, square array read by ascending antidiagonals (n >= 0, k >= 1). 1
1, 1, 2, 1, 3, 3, 1, 4, 6, 4, 1, 5, 11, 10, 5, 1, 6, 18, 26, 15, 6, 1, 7, 27, 58, 57, 21, 7, 1, 8, 38, 112, 179, 120, 28, 8, 1, 9, 51, 194, 453, 543, 247, 36, 9, 1, 10, 66, 310, 975, 1818, 1636, 502, 45, 10, 1, 11, 83, 466, 1865, 4881, 7279, 4916, 1013, 55, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(1,k) = k*(k + 1)/2, and T(n,k) = (k - (k + 1)*n + n^(k + 1))/(n^2 - 2*n + 1) elsewhere.

T(n,k) = third entry in the vector M^k * (1, 0, 0), where M is the following 3 X 3 matrix:

  1, 0, 0

  1, 1, 0

  1, 1, n.

EXAMPLE

Square array begins:

  n\k | 1   2   3   4    5     6      7       8 ...

  -------------------------------------------------

    0 | 1   2   3   4    5     6      7       8 ... A000027

    1 | 1   3   6  10   15    21     28      36 ... A000217

    2 | 1   4  11  26   57   120    247     502 ... A000295

    3 | 1   5  18  58  179   543   1636    4916 ... A000340

    4 | 1   6  27 112  453  1818   7279   29124 ... A014825

    5 | 1   7  38 194  975  4881  24412  122068 ... A014827

    6 | 1   8  51 310 1865 11196  67183  403106 ... A014829

    7 | 1   9  66 466 3267 22875 160132 1120932 ... A014830

    8 | 1  10  83 668 5349 42798 342391 2739136 ... A014831

    ...

PROG

(Maxima)

T(n, k) := if k = 1 then 1 else n*T(n, k - 1) + k$

create_list(T(n - k + 1, k), n, 0, 20, k, 1, n + 1);

/* Franck Maminirina Ramaharo, Jan 26 2019 */

CROSSREFS

Antidiagonal sums: A134195. - Gary W. Adamson, Oct 12 2007

Cf. A000027, A000217, A000295, A000340, A014825, A014827, A014829, A014830, A014831.

Sequence in context: A034356 A075195 A293311 * A239986 A285548 A130305

Adjacent sequences:  A126882 A126883 A126884 * A126886 A126887 A126888

KEYWORD

nonn,easy,tabl

AUTHOR

Gary W. Adamson, Dec 30 2006

EXTENSIONS

Edited and name clarified by Franck Maminirina Ramaharo, Jan 26 2019

STATUS

approved

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Last modified October 21 11:42 EDT 2019. Contains 328296 sequences. (Running on oeis4.)