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Expansion of (1+6x)/(1-x)^10.
2

%I #24 Sep 08 2022 08:45:01

%S 1,16,115,550,2035,6292,17017,41470,92950,194480,384098,722228,

%T 1301690,2261000,3801710,6210644,9887999,15382400,23434125,35027850,

%U 51456405,74397180,106002975,149009250,206859900,283853856,385314996,517788040

%N Expansion of (1+6x)/(1-x)^10.

%C Partial sums of A034266. - _Vladimir Joseph Stephan Orlovsky_, Jun 25 2009

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

%H Vincenzo Librandi, <a href="/A055994/b055994.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1)

%F a(n) = (7n+9)*C(n+8, 8)/9.

%F G.f.: (1+6x)/(1-x)^10.

%t CoefficientList[Series[(1 + 6 x)/(1 - x)^10, {x, 0, 50}], x] (* _Vincenzo Librandi_, Jul 30 2014 *)

%t LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,16,115,550,2035,6292,17017,41470,92950,194480},30] (* _Harvey P. Dale_, Sep 07 2022 *)

%o (Magma) [((7*n+9)*Binomial(n+8,8))/9: n in [0..40]]; // _Vincenzo Librandi_, Jul 30 2014

%Y Cf. A034266.

%Y Cf. A093564 ((7, 1) Pascal, column m=9). Partial sums of A034266.

%K easy,nonn

%O 0,2

%A _Barry E. Williams_, Jun 04 2000