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).

1, 4, 10, -24, -420, -960, 22680, 201600, -1496880, -36288000, 64864800, 7823692800, 25297272000, -2092278988800, -18988521552000, 690452066304000, 11457025515936000, -277436193914880000, -7430805000755136000, 133809610449715200000, 5500591866494524800000, -76432049488877322240000

Offset: 0

Author

Vincent v.d. Noort, Mar 21 2007

Keywords

• sign

References

• V. van der Noort and N. J. A. Sloane, Paper in preparation, 2007.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..150

Crossrefs

A column of A105937.

Programs

Magma

function T(n, k)
  if k eq 0 then return 1;
  elif k eq 1 then return n;
  else return (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2);
  end if; return T; end function;
[T(4, n): n in [0..25]]; // G. C. Greubel, Jan 29 2020

Maple

T:= proc(n, k) option remember;
      if k=0 then 1
    elif k=1 then n
    else (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2)
      fi; end:
seq(T(4, n), n=0..25); # G. C. Greubel, Jan 29 2020

Mathematica

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 *)

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) ));
vector(25, n, T(4, (n-1)) ) \\ G. C. Greubel, Jan 29 2020

Sage

@CachedFunction
def T(n, k):
    if (k==0): return 1
    elif (k==1): return n
    else: return (n-k+1)*T(n+1, k-1) - (k-1)*(n+1)*T(n+2, k-2)
[T(4, n) for n in (0..25)] # G. C. Greubel, Jan 29 2020