A127145 Q(3,n), where Q(m,k) is defined in A127080 and A127137.
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
Offset: 0
Keywords
References
- V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
Links
- G. C. Greubel, Table of n, a(n) for n = 0..500
Programs
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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 *) -
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
Formula
See A127080 for e.g.f.