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A307668 A(n,k) = Sum_{j=0..floor(n/k)} (-1)^j*binomial(2*n,k*j+n), square array A(n,k) read by antidiagonals, for n >= 0, k >= 1. 1
1, 1, 1, 1, 2, 3, 1, 2, 5, 10, 1, 2, 6, 14, 35, 1, 2, 6, 19, 43, 126, 1, 2, 6, 20, 62, 142, 462, 1, 2, 6, 20, 69, 207, 494, 1716, 1, 2, 6, 20, 70, 242, 705, 1780, 6435, 1, 2, 6, 20, 70, 251, 858, 2445, 6563, 24310, 1, 2, 6, 20, 70, 252, 912, 3068, 8622, 24566, 92378 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

LINKS

Table of n, a(n) for n=0..65.

EXAMPLE

Square array begins:

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

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

      3,    5,    6,     6,     6,     6,     6, ...

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

     35,   43,   62,    69,    70,    70,    70, ...

    126,  142,  207,   242,   251,   252,   252, ...

    462,  494,  705,   858,   912,   923,   924, ...

   1716, 1780, 2445,  3068,  3341,  3418,  3431, ...

   6435, 6563, 8622, 11051, 12310, 12750, 12854, ...

MATHEMATICA

T[n_, k_] := Sum[(-1)^j*Binomial[2*n, k*j + n], {j, 0, Floor[n/k]}]; Table[T[n - k, k], {n, 0, 11}, {k, n, 1, -1}] // Flatten (* Amiram Eldar, May 13 2021*)

CROSSREFS

Columns 1-2 give A088218, A005317.

Cf. A306914, A307039, A307394, A307665.

Sequence in context: A109202 A245559 A117488 * A308173 A256910 A181176

Adjacent sequences:  A307665 A307666 A307667 * A307669 A307670 A307671

KEYWORD

nonn,tabl

AUTHOR

Seiichi Manyama, Apr 20 2019

STATUS

approved

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Last modified October 7 16:02 EDT 2022. Contains 357275 sequences. (Running on oeis4.)