A127138 Q(1,n), where Q(m,k) is defined in A127080 and A127137.

1, 1, -1, -4, 3, 28, -15, -288, 105, 3984, -945, -70080, 10395, 1506240, -135135, -38384640, 2027025, 1133072640, -34459425, -38038533120, 654729075, 1431213235200, -13749310575, -59645279232000, 316234143225, 2726781752217600, -7905853580625, -135661078090137600, 213458046676875

Offset: 0

Author

N. J. A. Sloane, Mar 24 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..500

Crossrefs

A001147 interleaved with A076729.

Column 1 of A127080.

Cf. A127137, A127144, A127145.

Programs

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(1, 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[1, k], {k,0,30}] (* G. C. Greubel, Jan 30 2020 *)

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

Formula

See A127080 for e.g.f.