A126958 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,4).

36, 24, -60, -216, -420, -624, -756, -720, -396, 360, 1716, 3864, 7020, 11424, 17340, 25056, 34884, 47160, 62244, 80520, 102396, 128304, 158700, 194064, 234900, 281736, 335124, 395640, 463884, 540480, 626076, 721344, 826980, 943704, 1072260, 1213416, 1367964

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 (5,-10,10,-5,1).

Crossrefs

A row of A105937.

Programs

GAP

List([0..40], n-> (n+3)*(n+1)*(n^2 -10*n +12)); # G. C. Greubel, Jan 29 2020

Magma

[(n+3)*(n+1)*(n^2 -10*n +12): n in [0..40]]; // G. C. Greubel, Jan 29 2020

Maple

seq( (n+3)*(n+1)*(n^2 -10*n +12), n=0..40); # G. C. Greubel, Jan 29 2020

Mathematica

Table[(n+3)*(n+1)*(n^2 -10*n +12), {n,0,40}] (* G. C. Greubel, Jan 29 2020 *)

PARI

vector(41, n, my(m=n-1); (m+3)*(m+1)*(m^2 -10*m +12)) \\ G. C. Greubel, Jan 29 2020

Sage

[(n+3)*(n+1)*(n^2 -10*n +12) for n in (0..40)] # G. C. Greubel, Jan 29 2020

Formula

a(n) = (n+3)*(n+1)*(n^2 -10*n +12).

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

G.f.: 12*(3 -13*x +15*x^2 -3*x^3)/(1-x)^5.

E.g.f.: (36 -12*x -36*x^2 +x^4)*exp(x). (End)