cp's OEIS Frontend

A127070 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(4,n).

%I A127070 #8 Sep 08 2022 08:45:29
%S A127070 1,4,10,-24,-420,-960,22680,201600,-1496880,-36288000,64864800,
%T A127070 7823692800,25297272000,-2092278988800,-18988521552000,
%U A127070 690452066304000,11457025515936000,-277436193914880000,-7430805000755136000,133809610449715200000,5500591866494524800000,-76432049488877322240000
%N A127070 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(4,n).
%D A127070 V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
%H A127070 G. C. Greubel, <a href="/A127070/b127070.txt">Table of n, a(n) for n = 0..150</a>
%p A127070 T:= proc(n, k) option remember;
%p A127070       if k=0 then 1
%p A127070     elif k=1 then n
%p A127070     else (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2)
%p A127070       fi; end:
%p A127070 seq(T(4, n), n=0..25); # _G. C. Greubel_, Jan 29 2020
%t A127070 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[4, n], {n,0,25}] (* _G. C. Greubel_, Jan 29 2020 *)
%o A127070 (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 A127070 vector(25, n, T(4, (n-1)) ) \\ _G. C. Greubel_, Jan 29 2020
%o A127070 (Magma)
%o A127070 function T(n, k)
%o A127070   if k eq 0 then return 1;
%o A127070   elif k eq 1 then return n;
%o A127070   else return (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2);
%o A127070   end if; return T; end function;
%o A127070 [T(4, n): n in [0..25]]; // _G. C. Greubel_, Jan 29 2020
%o A127070 (Sage)
%o A127070 @CachedFunction
%o A127070 def T(n, k):
%o A127070     if (k==0): return 1
%o A127070     elif (k==1): return n
%o A127070     else: return (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2)
%o A127070 [T(4, n) for n in (0..25)] # _G. C. Greubel_, Jan 29 2020
%Y A127070 A column of A105937.
%K A127070 sign
%O A127070 0,2
%A A127070 Vincent v.d. Noort, Mar 21 2007