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A321163 Square array A(n,k), n >= 1, k >= 1, read by antidiagonals, where A(n,k) is the sum of distinct products Product_{j=1..k} b_j with 1 <= b_j<= n. 4
1, 1, 3, 1, 7, 6, 1, 15, 25, 10, 1, 31, 90, 61, 15, 1, 63, 301, 310, 136, 21, 1, 127, 966, 1441, 990, 244, 28, 1, 255, 3025, 6370, 6391, 2220, 440, 36, 1, 511, 9330, 27301, 38325, 17731, 5300, 680, 45, 1, 1023, 28501, 114670, 218926, 130851, 54831, 9660, 1022, 55 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Seiichi Manyama, Antidiagonals n = 1..25, flattened

EXAMPLE

In case of (n,k) = (3,2):

  | 1  2  3

--+--------

1 | 1, 2, 3

2 | 2, 4, 6

3 | 3, 6, 9

Distinct products are 1,2,3,4,6,9. So A(3,2) = 1+2+3+4+6+9 = 25.

Square array begins:

    1,    1,     1,      1,       1,        1, ...

    3,    7,    15,     31,      63,      127, ...

    6,   25,    90,    301,     966,     3025, ...

   10,   61,   310,   1441,    6370,    27301, ...

   15,  136,   990,   6391,   38325,   218926, ...

   21,  244,  2220,  17731,  130851,   916714, ...

   28,  440,  5300,  54831,  514668,  4519390, ...

   36,  680,  9660, 116991, 1280916, 13092430, ...

   45, 1022, 17130, 242091, 3070935, 36184072, ...

   55, 1472, 28670, 467391, 6807045, 91765822, ...

CROSSREFS

Columns 1-3 give A000217, A321165, A323334.

Rows 1-2 give A000012, A000225(n+1).

Main diagonal gives A321164.

Cf. A322967.

Row 3 gives A000392(n+4). - Fred Daniel Kline, Jan 11 2019

Sequence in context: A275662 A110441 A111806 * A054458 A110168 A323663

Adjacent sequences:  A321160 A321161 A321162 * A321164 A321165 A321166

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Jan 10 2019

STATUS

approved

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Last modified March 26 18:36 EDT 2019. Contains 321511 sequences. (Running on oeis4.)