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%I #10 Jan 31 2020 07:15:26
%S 1,1,-1,-4,3,28,-15,-288,105,3984,-945,-70080,10395,1506240,-135135,
%T -38384640,2027025,1133072640,-34459425,-38038533120,654729075,
%U 1431213235200,-13749310575,-59645279232000,316234143225,2726781752217600,-7905853580625,-135661078090137600,213458046676875
%N Q(1,n), where Q(m,k) is defined in A127080 and A127137,
%D V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
%H G. C. Greubel, <a href="/A127138/b127138.txt">Table of n, a(n) for n = 0..500</a>
%F See A127080 for e.g.f.
%p Q:= proc(n, k) option remember;
%p if k<2 then 1
%p elif `mod`(k,2)=0 then (n-k+1)*Q(n+1,k-1) - (k-1)*Q(n+2,k-2)
%p else ( (n-k+1)*Q(n+1,k-1) - (k-1)*(n+1)*Q(n+2,k-2) )/n
%p fi; end;
%p seq( Q(1, n), n=0..30); # _G. C. Greubel_, Jan 30 2020
%t 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 (Sage)
%o @CachedFunction
%o def Q(n,k):
%o if (k<2): return 1
%o elif (mod(k,2)==0): return (n-k+1)*Q(n+1,k-1) - (k-1)*Q(n+2,k-2)
%o else: return ( (n-k+1)*Q(n+1,k-1) - (k-1)*(n+1)*Q(n+2,k-2) )/n
%o [Q(1,n) for n in (0..30)] # _G. C. Greubel_, Jan 30 2020
%Y A001147 interleaved with A076729.
%Y Column 1 of A127080.
%Y Cf. A127137, A127144, A127145.
%K sign
%O 0,4
%A _N. J. A. Sloane_, Mar 24 2007
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