A247490 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).

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

Offset

0,13

Links

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

Example

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.

Maple

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);

Prog

(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)])

Crossrefs

Cf. A000166, A000255, A000153, A000261, A001909, A001910, A176732 - A176736.

Sequence in context: A289813 A050075 A350110 * A002120 A021435 A334358

Adjacent sequences: A247487 A247488 A247489 * A247491 A247492 A247493

Keyword

nonn,tabl

Author

Peter Luschny, Sep 20 2014

Status

approved