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A247504 Square array read by antidiagonals, A(n,k) = k!*[x^k]((1-Sum_{j=1..n} x^j)^(-1)), (n>=0,k>=0). 0
1, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 4, 6, 0, 1, 1, 4, 18, 24, 0, 1, 1, 4, 24, 120, 120, 0, 1, 1, 4, 24, 168, 960, 720, 0, 1, 1, 4, 24, 192, 1560, 9360, 5040, 0, 1, 1, 4, 24, 192, 1800, 17280, 105840, 40320, 0, 1, 1, 4, 24, 192, 1920, 20880, 221760, 1370880, 362880, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,9

LINKS

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

EXAMPLE

n\k[0][1][2] [3]  [4]   [5]    [6]     [7]      [8]       [9]

[0] 1, 0, 0,  0,   0,    0,     0,      0,       0,        0

[1] 1, 1, 2,  6,  24,  120,   720,   5040,   40320,   362880 [A000142]

[2] 1, 1, 4, 18, 120,  960,  9360, 105840, 1370880, 19958400 [A005442]

[3] 1, 1, 4, 24, 168, 1560, 17280, 221760, 3265920, 54069120

[.] .  .  .  .  .   .   .   .    .    .    .     .     .

oo] 1, 1, 4, 24, 192, 1920, 23040, 322560, 5160960, 92897280 [A002866]

'

As a triangular array, starts:

1,

1, 0,

1, 1, 0,

1, 1, 2, 0,

1, 1, 4, 6,  0,

1, 1, 4, 18, 24,  0,

1, 1, 4, 24, 120, 120, 0,

1, 1, 4, 24, 168, 960, 720, 0.

MAPLE

A := (n, k) -> k!*coeff(series((1-add(x^j, j=1..n))^(-1), x, k+2), x, k): seq(print(seq(A(n, k), k=0..9)), n=0..7);

CROSSREFS

Cf. A247505, A247506, A002866, A000142, A005442.

Sequence in context: A215703 A292712 A331571 * A306800 A235955 A077762

Adjacent sequences:  A247501 A247502 A247503 * A247505 A247506 A247507

KEYWORD

nonn,tabl

AUTHOR

Peter Luschny, Nov 03 2014

STATUS

approved

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Last modified September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)