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A127145 Q(3,n), where Q(m,k) is defined in A127080 and A127137, 4
1, 1, 1, -2, -9, 4, 75, 24, -735, -816, 8505, 17760, -114345, -388800, 1756755, 9233280, -30405375, -242968320, 585810225, 7125511680, -12439852425, -232838323200, 288735522075, 8450546227200, -7273385294175, -339004760371200, 197646339515625, 14945696794828800, -5763367260275625 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
REFERENCES
V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
LINKS
FORMULA
See A127080 for e.g.f.
MAPLE
Q:= proc(n, k) option remember;
if k<2 then 1
elif `mod`(k, 2)=0 then (n-k+1)*Q(n+1, k-1) - (k-1)*Q(n+2, k-2)
else ( (n-k+1)*Q(n+1, k-1) - (k-1)*(n+1)*Q(n+2, k-2) )/n
fi; end;
seq( Q(3, n), n=0..30); # G. C. Greubel, Jan 30 2020
MATHEMATICA
Q[n_, k_]:= Q[n, k]= If[k<2, 1, If[EvenQ[k], (n-k+1)*Q[n+1, k-1] - (k-1)*Q[n + 2, k-2], ((n-k+1)*Q[n+1, k-1] - (k-1)*(n+1)*Q[n+2, k-2])/n]]; Table[Q[3, k], {k, 0, 30}] (* G. C. Greubel, Jan 30 2020 *)
PROG
(Sage)
@CachedFunction
def Q(n, k):
if (k<2): return 1
elif (mod(k, 2)==0): return (n-k+1)*Q(n+1, k-1) - (k-1)*Q(n+2, k-2)
else: return ( (n-k+1)*Q(n+1, k-1) - (k-1)*(n+1)*Q(n+2, k-2) )/n
[Q(3, n) for n in (0..30)] # G. C. Greubel, Jan 30 2020
CROSSREFS
Cf. A126965.
Column 3 of A127080.
Sequence in context: A268249 A268246 A268103 * A210423 A003725 A292952
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Mar 24 2007
STATUS
approved

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Last modified March 28 13:25 EDT 2024. Contains 371254 sequences. (Running on oeis4.)