A127145 Q(3,n), where Q(m,k) is defined in A127080 and A127137,

1, 1, 1, -2, -9, 4, 75, 24, -735, -816, 8505, 17760, -114345, -388800, 1756755, 9233280, -30405375, -242968320, 585810225, 7125511680, -12439852425, -232838323200, 288735522075, 8450546227200, -7273385294175, -339004760371200, 197646339515625, 14945696794828800, -5763367260275625

Offset

0,4

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..500

Formula

See A127080 for e.g.f.

Maple

Q:= proc(n, k) option remember;
      if k<2 then 1
    elif `mod`(k, 2)=0 then (n-k+1)*Q(n+1, k-1) - (k-1)*Q(n+2, k-2)
    else ( (n-k+1)*Q(n+1, k-1) - (k-1)*(n+1)*Q(n+2, k-2) )/n
      fi; end;
seq( Q(3, n), n=0..30); # G. C. Greubel, Jan 30 2020

Mathematica

Q[n_, k_]:= Q[n, k]= If[k<2, 1, If[EvenQ[k], (n-k+1)*Q[n+1, k-1] - (k-1)*Q[n + 2, k-2], ((n-k+1)*Q[n+1, k-1] - (k-1)*(n+1)*Q[n+2, k-2])/n]]; Table[Q[3, k], {k, 0, 30}] (* G. C. Greubel, Jan 30 2020 *)

Prog

(Sage)
@CachedFunction
def Q(n, k):
    if (k<2): return 1
    elif (mod(k, 2)==0): return (n-k+1)*Q(n+1, k-1) - (k-1)*Q(n+2, k-2)
    else: return ( (n-k+1)*Q(n+1, k-1) - (k-1)*(n+1)*Q(n+2, k-2) )/n
[Q(3, n) for n in (0..30)] # G. C. Greubel, Jan 30 2020

Crossrefs

Cf. A126965.

Column 3 of A127080.

Cf. A127137, A127138, A127144.

Sequence in context: A268249 A268246 A268103 * A210423 A003725 A292952

Adjacent sequences: A127142 A127143 A127144 * A127146 A127147 A127148

Keyword

sign

Author

N. J. A. Sloane, Mar 24 2007

Status

approved