A163832 a(n) = n*(2*n^2 + 5*n + 1).
0, 8, 38, 102, 212, 380, 618, 938, 1352, 1872, 2510, 3278, 4188, 5252, 6482, 7890, 9488, 11288, 13302, 15542, 18020, 20748, 23738, 27002, 30552, 34400, 38558, 43038, 47852, 53012, 58530, 64418, 70688, 77352, 84422, 91910, 99828, 108188, 117002
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Crossrefs
Cf. A155156.
Programs
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Mathematica
Table[n(2n^2+5n+1),{n,0,40}] (* or *) LinearRecurrence[{4,-6,4,-1},{0,8,38,102},40] (* Harvey P. Dale, Feb 02 2012 *) -
PARI
for(n=0, 40, print1(n*(2*n^2+5*n+1)", ")); \\ Vincenzo Librandi, Feb 22 2012
Formula
G.f.: -2*x*(1+x)*(x-4)/(x-1)^4.
a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4).
a(n) = -n*A168244(n+2). - Bruno Berselli, Feb 02 2012
E.g.f.: x*(8 + 11*x + 2*x^2)*exp(x). - G. C. Greubel, Aug 05 2017
Extensions
Edited by R. J. Mathar, Aug 05 2009
Comments