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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). 2
1, 4, 10, -24, -420, -960, 22680, 201600, -1496880, -36288000, 64864800, 7823692800, 25297272000, -2092278988800, -18988521552000, 690452066304000, 11457025515936000, -277436193914880000, -7430805000755136000, 133809610449715200000, 5500591866494524800000, -76432049488877322240000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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(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 *)

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(4, (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(4, 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(4, n) for n in (0..25)] # G. C. Greubel, Jan 29 2020

CROSSREFS

A column of A105937.

Sequence in context: A217696 A223014 A038783 * A107961 A051864 A111153

Adjacent sequences:  A127067 A127068 A127069 * A127071 A127072 A127073

KEYWORD

sign

AUTHOR

Vincent v.d. Noort, Mar 21 2007

STATUS

approved

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Last modified March 29 02:19 EDT 2020. Contains 333104 sequences. (Running on oeis4.)