A037250 a(n) = n^2*(n^2 + 1)*(n-1).

0, 0, 20, 180, 816, 2600, 6660, 14700, 29120, 53136, 90900, 147620, 229680, 344760, 501956, 711900, 986880, 1340960, 1790100, 2352276, 3047600, 3898440, 4929540, 6168140, 7644096, 9390000, 11441300

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Conjecture: satisfies a linear recurrence having signature (6, -15, 20, -15, 6, -1). - Harvey P. Dale, Jul 27 2019

This conjecture is true since for any series a(n) = P(n) (P polynomial in n of degree d) there is an o.g.f. Q(x)/(1-x)^(d+1). - Georg Fischer, Feb 17 2021

References

• R. W. Carter, Simple Groups of Lie Type, Wiley 1972, Chap. 14.
• J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A064487, A064583.

Programs

Magma

[n^2*(n^2+1)*(n-1): n in [0..30]]; // Vincenzo Librandi, Sep 14 2011

Maple

seq(coeff(series(4*x^2*(x^3+9*x^2+15*x+5)/(x-1)^6, x, n+1),x,n), n = 0..30); # Georg Fischer, Feb 17 2021

Mathematica

Table[n^2 (n^2+1)(n-1),{n,0,30}] (* Harvey P. Dale, Jul 27 2019 *)