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Expansion of (3+x)/(1-x)^6.
2

%I #14 Apr 16 2023 20:45:11

%S 3,19,69,189,434,882,1638,2838,4653,7293,11011,16107,22932,31892,

%T 43452,58140,76551,99351,127281,161161,201894,250470,307970,375570,

%U 454545,546273,652239,774039,913384,1072104,1252152,1455608,1684683,1941723

%N Expansion of (3+x)/(1-x)^6.

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = binomial(n+4, 4)*(15+4*n)/5.

%F G.f.: (3+x)/(1-x)^6.

%F a(-n-4) = -A034263(n). - _Bruno Berselli_, Aug 23 2011

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6). - _Wesley Ivan Hurt_, Apr 16 2023

%t f[n_]:=Binomial[n+4,4]*(15+4*n)/5; Table[f[n],{n,0,5!}] (* _Vladimir Joseph Stephan Orlovsky_, May 30 2010 *)

%Y Cf. A034263.

%K nonn,easy

%O 0,1

%A _Wolfdieter Lang_, Feb 02 2001

%E More terms from _Vladimir Joseph Stephan Orlovsky_, May 30 2010