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A247490
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Square array read by antidiagonals: A(k, n) = (-1)^(n+1)* hypergeom([k, -n+1], [], 1) for n>0 and A(k,0) = 0 (n>=0, k>=1).
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1
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0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 0, 1, 2, 3, 2, 0, 1, 3, 7, 11, 9, 0, 1, 4, 13, 32, 53, 44, 0, 1, 5, 21, 71, 181, 309, 265, 0, 1, 6, 31, 134, 465, 1214, 2119, 1854, 0, 1, 7, 43, 227, 1001, 3539, 9403, 16687, 14833, 0, 1, 8, 57, 356, 1909, 8544, 30637, 82508, 148329, 133496
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OFFSET
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0,13
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LINKS
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Table of n, a(n) for n=0..65.
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EXAMPLE
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k\n
[1], 0, 1, 0, 1, 2, 9, 44, 265, 1854, ... A000166
[2], 0, 1, 1, 3, 11, 53, 309, 2119, 16687, ... A000255
[3], 0, 1, 2, 7, 32, 181, 1214, 9403, 82508, ... A000153
[4], 0, 1, 3, 13, 71, 465, 3539, 30637, 296967, ... A000261
[5], 0, 1, 4, 21, 134, 1001, 8544, 81901, 870274, ... A001909
[6], 0, 1, 5, 31, 227, 1909, 18089, 190435, 2203319, ... A001910
[7], 0, 1, 6, 43, 356, 3333, 34754, 398959, 4996032, ... A176732
[8], 0, 1, 7, 57, 527, 5441, 61959, 770713, 10391023, ... A176733
The referenced sequences may have a different offset or other small deviations.
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MAPLE
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A := (k, n) -> `if`(n<2, n, hypergeom([k, -n+1], [], 1)*(-1)^(n+1));
seq(print(seq(round(evalf(A(k, n), 100)), n=0..8)), k=1..8);
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PROG
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(Sage)
from mpmath import mp, hyp2f0
mp.dps = 25; mp.pretty = True
def A247490(k, n):
if n < 2: return n
if k == 1 and n == 2: return 0 # (failed to converge)
return int((-1)^(n+1)*hyp2f0(k, -n+1, 1))
for k in (1..8): print([k], [A247490(k, n) for n in (0..8)])
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CROSSREFS
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Cf. A000166, A000255, A000153, A000261, A001909, A001910, A176732 - A176736.
Sequence in context: A071493 A289813 A050075 * A002120 A021435 A334358
Adjacent sequences: A247487 A247488 A247489 * A247491 A247492 A247493
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KEYWORD
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nonn,tabl
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AUTHOR
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Peter Luschny, Sep 20 2014
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STATUS
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approved
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