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A307394 Square array A(n,k), n >= 0, k >= 1, read by antidiagonals, where column k is the expansion of g.f. ((1-x)^(k-4))/((1-x)^k+x^k). 5
1, 1, 3, 1, 4, 6, 1, 4, 9, 10, 1, 4, 10, 14, 15, 1, 4, 10, 19, 15, 21, 1, 4, 10, 20, 28, 8, 28, 1, 4, 10, 20, 34, 28, -7, 36, 1, 4, 10, 20, 35, 48, 1, -22, 45, 1, 4, 10, 20, 35, 55, 48, -80, -21, 55, 1, 4, 10, 20, 35, 56, 75, 0, -242, 12, 66, 1, 4, 10, 20, 35, 56, 83, 75, -164, -485, 77, 78 (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..floor(n/k)} (-1)^j * binomial(n+3,k*j+3).

A(n,2*k) = Sum_{i=0..n} Sum_{j=0..n-i} (-1)^j * binomial(i+1,k*j+1) * binomial(n-i+1,k*j+1).

EXAMPLE

Square array begins:

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

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

    6,   9,   10,   10, 10,  10,  10,  10,  10, ...

   10,  14,   19,   20, 20,  20,  20,  20,  20, ...

   15,  15,   28,   34, 35,  35,  35,  35,  35, ...

   21,   8,   28,   48, 55,  56,  56,  56,  56, ...

   28,  -7,    1,   48, 75,  83,  84,  84,  84, ...

   36, -22,  -80,    0, 75, 110, 119, 120, 120, ...

   45, -21, -242, -164,  0, 110, 154, 164, 165, ...

CROSSREFS

Columns 1-5 give A000217(n+1), A279230, A307395, A099589(n+3), A289388(n+3).

Cf. A306914, A307039, A307079, A307393.

Sequence in context: A051203 A243553 A286159 * A194540 A193043 A086271

Adjacent sequences:  A307391 A307392 A307393 * A307395 A307396 A307397

KEYWORD

sign,tabl

AUTHOR

Seiichi Manyama, Apr 07 2019

STATUS

approved

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Last modified April 18 19:31 EDT 2021. Contains 343089 sequences. (Running on oeis4.)