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A306245 Square array A(n,k), n>=0, k>=0, read by antidiagonals, where A(0,k) = 1 and A(n,k) = Sum_{j=0..n-1} k^j * binomial(n-1,j) * A(j,k) for n > 0. 2
1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 3, 5, 1, 1, 1, 4, 17, 15, 1, 1, 1, 5, 43, 179, 52, 1, 1, 1, 6, 89, 1279, 3489, 203, 1, 1, 1, 7, 161, 5949, 108472, 127459, 877, 1, 1, 1, 8, 265, 20591, 1546225, 26888677, 8873137, 4140, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

Seiichi Manyama, Antidiagonals n = 0..55, flattened

EXAMPLE

Square array begins:

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

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

   1,  2,    3,      4,       5,        6, ...

   1,  5,   17,     43,      89,      161, ...

   1, 15,  179,   1279,    5949,    20591, ...

   1, 52, 3489, 108472, 1546225, 12950796, ...

MAPLE

A:= proc(n, k) option remember; `if`(n=0, 1,

      add(k^j*binomial(n-1, j)*A(j, k), j=0..n-1))

    end:

seq(seq(A(n, d-n), n=0..d), d=0..12);  # Alois P. Heinz, Jul 28 2019

CROSSREFS

Columns k=0..2 give A000012, A000110, A126443.

Rows n=0+1, 2 give A000012, A000027(n+1).

Main diagonal gives A309401.

Cf. A309386.

Sequence in context: A144150 A124560 A290759 * A275043 A227061 A201949

Adjacent sequences:  A306242 A306243 A306244 * A306246 A306247 A306248

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Jul 28 2019

STATUS

approved

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Last modified December 8 17:36 EST 2019. Contains 329865 sequences. (Running on oeis4.)