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).

1, 1, -2, -12, 24, 420, -720, -30240, 40320, 3764880, -3628800, -728481600, 479001600, 203545742400, -87178291200, -77806624896000, 20922789888000, 39045031657632000, -6402373705728000, -24904933604014464000, 2432902008176640000, 19678195269815322240000, -1124000727777607680000

Offset

0,3

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

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(1, 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[1, n], {n, 0, 25}] (* G. C. Greubel, Jan 29 2020 *)

Prog

(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(1, (n-1)) ) \\ G. C. Greubel, Jan 29 2020
(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(1, n): n in [0..25]]; // 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(1, n) for n in (0..25)] # G. C. Greubel, Jan 29 2020

Crossrefs

A column of A105937.

Sequence in context: A176710 A141900 A211374 * A002207 A181814 A232248

Adjacent sequences: A126959 A126960 A126961 * A126963 A126964 A126965

Keyword

sign

Author

Vincent v.d. Noort, Mar 21 2007

Status

approved