A126935 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(n,3).

0, -12, -24, -30, -24, 0, 48, 126, 240, 396, 600, 858, 1176, 1560, 2016, 2550, 3168, 3876, 4680, 5586, 6600, 7728, 8976, 10350, 11856, 13500, 15288, 17226, 19320, 21576, 24000, 26598, 29376, 32340, 35496, 38850, 42408, 46176, 50160, 54366, 58800, 63468, 68376, 73530

Offset: 0

Author

Vincent v.d. Noort, Mar 21 2007

Keywords

• sign
• easy

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..1000
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Crossrefs

A row of A105937.

Programs

Magma

[n*(n+2)*(n-5): n in [0..50]]; // G. C. Greubel, Jan 29 2020

Maple

seq( n*(n+2)*(n-5), n=0..50); # 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[n, 3], {n,0,50}] (* G. C. Greubel, Jan 29 2020 *)

PARI

vector(50, n, my(m=n-1); m*(m+2)*(m-5) ) \\ G. C. Greubel, Jan 29 2020

Sage

[n*(n+2)*(n-5) for n in (0..50)] # G. C. Greubel, Jan 29 2020

Formula

a(n) = n*(n+2)*(n-5).

From G. C. Greubel, Jan 29 2020: (Start)

G.f.: (-6)*x*(2 - 4*x + x^2)/(1-x)^4.

E.g.f.: x*(-12 + x^2)*exp(x). (End)