cp's OEIS Frontend

A127067 Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(2,n).

%I A127067 #6 Sep 08 2022 08:45:29
%S A127067 1,2,0,-24,-60,720,5040,-40320,-589680,3628800,99792000,-479001600,
%T A127067 -23740516800,87178291200,7682586912000,-20922789888000,
%U A127067 -3281772285792000,6402373705728000,1801868049805824000,-2432902008176640000,-1241948957556827520000,1124000727777607680000
%N A127067 Define an array by d(m, 0) = 1, d(m, 1) = m; d(m, k) = (m - k + 1) d(m+1, k-1) - (k-1) (m+1) d(m+2, k-2). Sequence gives d(2,n).
%D A127067 V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
%H A127067 G. C. Greubel, <a href="/A127067/b127067.txt">Table of n, a(n) for n = 0..350</a>
%p A127067 T:= proc(n, k) option remember;
%p A127067       if k=0 then 1
%p A127067     elif k=1 then n
%p A127067     else (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2)
%p A127067       fi; end:
%p A127067 seq(T(2, n), n=0..25); # _G. C. Greubel_, Jan 30 2020
%t A127067 T[n_, k_]:= T[n, k]= If[k==0, 1, If[k==1, n, (n-k+1)*T[n+1, k-1] - (k-1)*(n+1)* T[n+2, k-2]]]; Table[T[2, n], {n,0,25}] (* _G. C. Greubel_, Jan 30 2020 *)
%o A127067 (PARI) T(n, k) = if(k==0, 1, if(k==1, n, (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2) ));
%o A127067 vector(25, n, T(2, n-1) ) \\ _G. C. Greubel_, Jan 30 2020
%o A127067 (Magma)
%o A127067 function T(n, k)
%o A127067   if k eq 0 then return 1;
%o A127067   elif k eq 1 then return n;
%o A127067   else return (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2);
%o A127067   end if; return T; end function;
%o A127067 [T(2, n): n in [0..25]]; // _G. C. Greubel_, Jan 30 2020
%o A127067 (Sage)
%o A127067 @CachedFunction
%o A127067 def T(n, k):
%o A127067     if (k==0): return 1
%o A127067     elif (k==1): return n
%o A127067     else: return (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2)
%o A127067 [T(2, n) for n in (0..25)] # _G. C. Greubel_, Jan 30 2020
%Y A127067 A column of A105937.
%K A127067 sign
%O A127067 0,2
%A A127067 Vincent v.d. Noort, Mar 21 2007