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A306680 Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of g.f. ((1-x)^(k-1))/((1-x)^k-x^(k+1)). 7
1, 1, 2, 1, 1, 3, 1, 1, 2, 4, 1, 1, 1, 3, 5, 1, 1, 1, 2, 5, 6, 1, 1, 1, 1, 4, 8, 7, 1, 1, 1, 1, 2, 7, 13, 8, 1, 1, 1, 1, 1, 5, 12, 21, 9, 1, 1, 1, 1, 1, 2, 11, 21, 34, 10, 1, 1, 1, 1, 1, 1, 6, 21, 37, 55, 11, 1, 1, 1, 1, 1, 1, 2, 16, 37, 65, 89, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Seiichi Manyama, Antidiagonals n = 0..139, flattened

FORMULA

A(n,k) = Sum_{j=0..n} binomial(n-j,k*j).

A(n,k) = A306713(k*n,k) for k > 0.

EXAMPLE

A(4,1) = A306713(4,1) = 5, A(4,2) = A306713(8,2) = 4.

Square array begins:

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

   2,  1,  1,  1,  1,  1, 1, 1, 1, ...

   3,  2,  1,  1,  1,  1, 1, 1, 1, ...

   4,  3,  2,  1,  1,  1, 1, 1, 1, ...

   5,  5,  4,  2,  1,  1, 1, 1, 1, ...

   6,  8,  7,  5,  2,  1, 1, 1, 1, ...

   7, 13, 12, 11,  6,  2, 1, 1, 1, ...

   8, 21, 21, 21, 16,  7, 2, 1, 1, ...

   9, 34, 37, 37, 36, 22, 8, 2, 1, ...

CROSSREFS

Columns 0-9 give A000027(n+1), A000045(n+1), A005251(n+1), A003522, A005676, A099132, A293169, A306721, A306752, A306753.

Cf. A306646, A306713, A306735.

Sequence in context: A205131 A175892 A010783 * A083312 A032435 A117502

Adjacent sequences:  A306677 A306678 A306679 * A306681 A306682 A306683

KEYWORD

nonn,tabl,look

AUTHOR

Seiichi Manyama, Mar 05 2019

STATUS

approved

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Last modified February 17 21:35 EST 2020. Contains 332006 sequences. (Running on oeis4.)