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A308497 Square array A(n,k), n >= 1, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. log(1 + Sum_{j>=1} binomial(j+k-1,k) * x^j/j). 2
1, 1, 0, 1, 1, 1, 1, 2, 2, 1, 1, 3, 5, 6, 8, 1, 4, 10, 15, 24, 26, 1, 5, 17, 34, 54, 120, 194, 1, 6, 26, 69, 104, 240, 720, 1142, 1, 7, 37, 126, 204, 200, 1350, 5040, 9736, 1, 8, 50, 211, 408, -330, -400, 9450, 40320, 81384, 1, 9, 65, 330, 794, -1704, -12510, -2800, 78120, 362880, 823392 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,8

LINKS

Seiichi Manyama, Antidiagonals n = 1..140, flattened

FORMULA

A(n,k) = (1/k!) * ((n+k-1)! - Sum_{j=1..n-1} binomial(n-1,j) * (j+k-1)! * A(n-j,k)).

EXAMPLE

Square array begins:

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

     0,   1,    2,    3,      4,      5, ...

     1,   2,    5,   10,     17,     26, ...

     1,   6,   15,   34,     69,    126, ...

     8,  24,   54,  104,    204,    408, ...

    26, 120,  240,  200,   -330,  -1704, ...

   194, 720, 1350, -400, -12510, -51696, ...

CROSSREFS

Columns k=0..3 give A089064, A000142(n-1), (-1)^(n+1) * A009383(n), A308499.

Sequence in context: A274887 A008302 A131791 * A010358 A155865 A156133

Adjacent sequences:  A308494 A308495 A308496 * A308498 A308499 A308500

KEYWORD

sign,tabl

AUTHOR

Seiichi Manyama, Jun 01 2019

STATUS

approved

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Last modified April 5 17:03 EDT 2020. Contains 333245 sequences. (Running on oeis4.)