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A127145 Q(3,n), where Q(m,k) is defined in A127080 and A127137.

%I A127145 #9 Jun 01 2025 17:00:07
%S A127145 1,1,1,-2,-9,4,75,24,-735,-816,8505,17760,-114345,-388800,1756755,
%T A127145 9233280,-30405375,-242968320,585810225,7125511680,-12439852425,
%U A127145 -232838323200,288735522075,8450546227200,-7273385294175,-339004760371200,197646339515625,14945696794828800,-5763367260275625
%N A127145 Q(3,n), where Q(m,k) is defined in A127080 and A127137.
%D A127145 V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
%H A127145 G. C. Greubel, <a href="/A127145/b127145.txt">Table of n, a(n) for n = 0..500</a>
%F A127145 See A127080 for e.g.f.
%p A127145 Q:= proc(n, k) option remember;
%p A127145       if k<2 then 1
%p A127145     elif `mod`(k,2)=0 then (n-k+1)*Q(n+1,k-1) - (k-1)*Q(n+2,k-2)
%p A127145     else ( (n-k+1)*Q(n+1,k-1) - (k-1)*(n+1)*Q(n+2,k-2) )/n
%p A127145       fi; end;
%p A127145 seq( Q(3, n), n=0..30); # _G. C. Greubel_, Jan 30 2020
%t A127145 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 *)
%o A127145 (Sage)
%o A127145 @CachedFunction
%o A127145 def Q(n,k):
%o A127145     if (k<2): return 1
%o A127145     elif (mod(k,2)==0): return (n-k+1)*Q(n+1,k-1) - (k-1)*Q(n+2,k-2)
%o A127145     else: return ( (n-k+1)*Q(n+1,k-1) - (k-1)*(n+1)*Q(n+2,k-2) )/n
%o A127145 [Q(3,n) for n in (0..30)] # _G. C. Greubel_, Jan 30 2020
%Y A127145 Cf. A126965.
%Y A127145 Column 3 of A127080.
%Y A127145 Cf. A127137, A127138, A127144.
%K A127145 sign
%O A127145 0,4
%A A127145 _N. J. A. Sloane_, Mar 24 2007