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A306646 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. (k+1-x^k)/(1-x^k-x^(k+1)). 11
2, 3, 1, 4, 0, 3, 5, 0, 2, 4, 6, 0, 0, 3, 7, 7, 0, 0, 3, 2, 11, 8, 0, 0, 0, 4, 5, 18, 9, 0, 0, 0, 4, 0, 5, 29, 10, 0, 0, 0, 0, 5, 3, 7, 47, 11, 0, 0, 0, 0, 5, 0, 7, 10, 76, 12, 0, 0, 0, 0, 0, 6, 0, 4, 12, 123, 13, 0, 0, 0, 0, 0, 6, 0, 4, 3, 17, 199 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

FORMULA

A(0,k) = k+1 and A(n,k) = n*Sum_{j=1..floor(n/k)} binomial(j,n-k*j)/j for n > 0.

A(n,k) = (k+1)*A306713(n,k) - A306713(n-k,k) for n >= k.

EXAMPLE

A(6,1) = 6*Sum_{j=1..6} binomial(j,6-j)/j = 6*(1/3+3/2+1+1/6) = 18.

A(6,2) = 6*Sum_{j=1..3} binomial(j,6-2*j)/j = 6*(1/2+1/3) = 5.

Square array begins:

    2,  3, 4, 5, 6, 7, 8, 9, 10, 11, ...

    1,  0, 0, 0, 0, 0, 0, 0,  0,  0, ...

    3,  2, 0, 0, 0, 0, 0, 0,  0,  0, ...

    4,  3, 3, 0, 0, 0, 0, 0,  0,  0, ...

    7,  2, 4, 4, 0, 0, 0, 0,  0,  0, ...

   11,  5, 0, 5, 5, 0, 0, 0,  0,  0, ...

   18,  5, 3, 0, 6, 6, 0, 0,  0,  0, ...

   29,  7, 7, 0, 0, 7, 7, 0,  0,  0, ...

   47, 10, 4, 4, 0, 0, 8, 8,  0,  0, ...

   76, 12, 3, 9, 0, 0, 0, 9,  9,  0, ...

CROSSREFS

Columns 1-9 give A000032, A001608, A050443, A087935, A087936, A306755, A306756, A306757, A306758.

Cf. A306713, A306735.

Sequence in context: A253257 A127412 A304791 * A152832 A211343 A039661

Adjacent sequences:  A306643 A306644 A306645 * A306647 A306648 A306649

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Mar 03 2019

STATUS

approved

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Last modified October 15 07:56 EDT 2019. Contains 328026 sequences. (Running on oeis4.)