A173785 Expansion of 2*(1 -4*x +14*x^2 +4*x^3 +9*x^4)/(1-x)^5.

2, 2, 18, 98, 338, 882, 1922, 3698, 6498, 10658, 16562, 24642, 35378, 49298, 66978, 89042, 116162, 149058, 188498, 235298, 290322, 354482, 428738, 514098, 611618, 722402, 847602, 988418, 1146098, 1321938, 1517282, 1733522, 1972098, 2234498

Offset: 0

Author

Michel Lagneau, Feb 24 2010

Keywords

• nonn
• easy

References

• Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Clark Kimberling, Complementary Equations, Journal of Integer Sequences, Vol. 10 (2007), Article 07.1.4.
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Crossrefs

Cf. A058031.

Programs

Maple

a:= n-> 2*(n^2-n+1)^2:
seq (a(n), n=0..40);

Mathematica

Table[2*(1-n+n^2)^2, {n,0,40}] (* G. C. Greubel, Jul 07 2021 *)
LinearRecurrence[{5,-10,10,-5,1},{2,2,18,98,338},50] (* Harvey P. Dale, Apr 20 2024 *)

PARI

a(n)=2*(n^2-n+1)^2 \\ Charles R Greathouse IV, Oct 21 2022

Sage

[2*(1-n+n^2)^2 for n in (0..40)] # G. C. Greubel, Jul 07 2021

Formula

G.f.: 2*(1 -4*x +14*x^2 +4*x^3 +9*x^4)/(1-x)^5.

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

a(n) = 2*A058031(n).

E.g.f.: 2*(1 + 4*x^2 + 4*x^3 + x^4)*exp(x). - G. C. Greubel, Jul 07 2021

Extensions

Edited by Alois P. Heinz, Feb 16 2012