A127144 Q(2,n), where Q(m,k) is defined in A127080 and A127137,

1, 1, 0, -3, -4, 15, 48, -105, -624, 945, 9600, -10395, -175680, 135135, 3790080, -2027025, -95235840, 34459425, 2752081920, -654729075, -90328089600, 13749310575, 3328103116800, -316234143225, -136191650918400, 7905853580625, 6131573025177600, -213458046676875, -301213549769932800

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(2, 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[2, 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(2, n) for n in (0..30)] # G. C. Greubel, Jan 30 2020

Crossrefs

A126967 interleaved with A001147.

Column 2 of A127080.

Cf. A127137, A127138, A127145.

Sequence in context: A332051 A209479 A209338 * A042771 A176755 A299684

Adjacent sequences: A127141 A127142 A127143 * A127145 A127146 A127147

Keyword

sign

Author

N. J. A. Sloane, Mar 24 2007

Status

approved