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A127144 Q(2,n), where Q(m,k) is defined in A127080 and A127137.

%I A127144 #13 Jun 01 2025 16:59:53
%S A127144 1,1,0,-3,-4,15,48,-105,-624,945,9600,-10395,-175680,135135,3790080,
%T A127144 -2027025,-95235840,34459425,2752081920,-654729075,-90328089600,
%U A127144 13749310575,3328103116800,-316234143225,-136191650918400,7905853580625,6131573025177600,-213458046676875,-301213549769932800
%N A127144 Q(2,n), where Q(m,k) is defined in A127080 and A127137.
%D A127144 V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
%H A127144 G. C. Greubel, <a href="/A127144/b127144.txt">Table of n, a(n) for n = 0..500</a>
%F A127144 See A127080 for e.g.f.
%p A127144 Q:= proc(n, k) option remember;
%p A127144       if k<2 then 1
%p A127144     elif `mod`(k,2)=0 then (n-k+1)*Q(n+1,k-1) - (k-1)*Q(n+2,k-2)
%p A127144     else ( (n-k+1)*Q(n+1,k-1) - (k-1)*(n+1)*Q(n+2,k-2) )/n
%p A127144       fi; end;
%p A127144 seq( Q(2, n), n=0..30); # _G. C. Greubel_, Jan 30 2020
%t A127144 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 *)
%o A127144 (Sage)
%o A127144 @CachedFunction
%o A127144 def Q(n,k):
%o A127144     if (k<2): return 1
%o A127144     elif (mod(k,2)==0): return (n-k+1)*Q(n+1,k-1) - (k-1)*Q(n+2,k-2)
%o A127144     else: return ( (n-k+1)*Q(n+1,k-1) - (k-1)*(n+1)*Q(n+2,k-2) )/n
%o A127144 [Q(2,n) for n in (0..30)] # _G. C. Greubel_, Jan 30 2020
%Y A127144 A126967 interleaved with A001147.
%Y A127144 Column 2 of A127080.
%Y A127144 Cf. A127137, A127138, A127145.
%K A127144 sign
%O A127144 0,4
%A A127144 _N. J. A. Sloane_, Mar 24 2007