cp's OEIS Frontend

A126962 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(1,n).

%I A126962 #9 Sep 08 2022 08:45:29
%S A126962 1,1,-2,-12,24,420,-720,-30240,40320,3764880,-3628800,-728481600,
%T A126962 479001600,203545742400,-87178291200,-77806624896000,20922789888000,
%U A126962 39045031657632000,-6402373705728000,-24904933604014464000,2432902008176640000,19678195269815322240000,-1124000727777607680000
%N A126962 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(1,n).
%D A126962 V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.
%H A126962 G. C. Greubel, <a href="/A126962/b126962.txt">Table of n, a(n) for n = 0..150</a>
%p A126962 T:= proc(n, k) option remember;
%p A126962       if k=0 then 1
%p A126962     elif k=1 then n
%p A126962     else (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2)
%p A126962       fi; end:
%p A126962 seq(T(1, n), n=0..25); # _G. C. Greubel_, Jan 29 2020
%t A126962 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[1, n], {n,0,25}] (* _G. C. Greubel_, Jan 29 2020 *)
%o A126962 (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 A126962 vector(25, n, T(1, (n-1)) ) \\ _G. C. Greubel_, Jan 29 2020
%o A126962 (Magma)
%o A126962 function T(n,k)
%o A126962   if k eq 0 then return 1;
%o A126962   elif k eq 1 then return n;
%o A126962   else return (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2);
%o A126962   end if; return T; end function;
%o A126962 [T(1,n): n in [0..25]]; // _G. C. Greubel_, Jan 29 2020
%o A126962 (Sage)
%o A126962 @CachedFunction
%o A126962 def T(n, k):
%o A126962     if (k==0): return 1
%o A126962     elif (k==1): return n
%o A126962     else: return (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2)
%o A126962 [T(1, n) for n in (0..25)] # _G. C. Greubel_, Jan 29 2020
%Y A126962 A column of A105937.
%K A126962 sign
%O A126962 0,3
%A A126962 Vincent v.d. Noort, Mar 21 2007