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A127144
Q(2,n), where Q(m,k) is defined in A127080 and A127137,
4
1, 1, 0, -3, -4, 15, 48, -105, -624, 945, 9600, -10395, -175680, 135135, 3790080, -2027025, -95235840, 34459425, 2752081920, -654729075, -90328089600, 13749310575, 3328103116800, -316234143225, -136191650918400, 7905853580625, 6131573025177600, -213458046676875, -301213549769932800
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(2, 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[2, 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(2, n) for n in (0..30)] # G. C. Greubel, Jan 30 2020
CROSSREFS
A126967 interleaved with A001147.
Column 2 of A127080.
Sequence in context: A332051 A209479 A209338 * A042771 A176755 A299684
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Mar 24 2007
STATUS
approved