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A127145 Q(3,n), where Q(m,k) is defined in A127080 and A127137, 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 20 00:50 EST 2021. Contains 340300 sequences. (Running on oeis4.)