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A127138 Q(1,n), where Q(m,k) is defined in A127080 and A127137, 4


%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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Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)