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A127138 Q(1,n), where Q(m,k) is defined in A127080 and A127137.

%I A127138 #12 Jun 01 2025 16:59:32
%S A127138 1,1,-1,-4,3,28,-15,-288,105,3984,-945,-70080,10395,1506240,-135135,
%T A127138 -38384640,2027025,1133072640,-34459425,-38038533120,654729075,
%U A127138 1431213235200,-13749310575,-59645279232000,316234143225,2726781752217600,-7905853580625,-135661078090137600,213458046676875
%N A127138 Q(1,n), where Q(m,k) is defined in A127080 and A127137.
%D A127138 V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
%H A127138 G. C. Greubel, <a href="/A127138/b127138.txt">Table of n, a(n) for n = 0..500</a>
%F A127138 See A127080 for e.g.f.
%p A127138 Q:= proc(n, k) option remember;
%p A127138       if k<2 then 1
%p A127138     elif `mod`(k,2)=0 then (n-k+1)*Q(n+1,k-1) - (k-1)*Q(n+2,k-2)
%p A127138     else ( (n-k+1)*Q(n+1,k-1) - (k-1)*(n+1)*Q(n+2,k-2) )/n
%p A127138       fi; end;
%p A127138 seq( Q(1, n), n=0..30); # _G. C. Greubel_, Jan 30 2020
%t A127138 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[1, k], {k,0,30}] (* _G. C. Greubel_, Jan 30 2020 *)
%o A127138 (Sage)
%o A127138 @CachedFunction
%o A127138 def Q(n,k):
%o A127138     if (k<2): return 1
%o A127138     elif (mod(k,2)==0): return (n-k+1)*Q(n+1,k-1) - (k-1)*Q(n+2,k-2)
%o A127138     else: return ( (n-k+1)*Q(n+1,k-1) - (k-1)*(n+1)*Q(n+2,k-2) )/n
%o A127138 [Q(1,n) for n in (0..30)] # _G. C. Greubel_, Jan 30 2020
%Y A127138 A001147 interleaved with A076729.
%Y A127138 Column 1 of A127080.
%Y A127138 Cf. A127137, A127144, A127145.
%K A127138 sign
%O A127138 0,4
%A A127138 _N. J. A. Sloane_, Mar 24 2007