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A053109 Expansion of 1/(1-10*x)^10.

%I A053109 #26 Oct 01 2023 12:31:42
%S A053109 1,100,5500,220000,7150000,200200000,5005000000,114400000000,
%T A053109 2431000000000,48620000000000,923780000000000,16796000000000000,
%U A053109 293930000000000000,4974200000000000000,81719000000000000000
%N A053109 Expansion of 1/(1-10*x)^10.
%C A053109 This is the tenth member of the k-family of sequences a(k,n) := k^n*binomial(n+k-1,k-1) starting with A000012 (powers of 1), A001787(n+1), A027472(n+3), A038846, A036071, A036084, A036226, A053107-9 for k=1..10.
%H A053109 G. C. Greubel, <a href="/A053109/b053109.txt">Table of n, a(n) for n = 0..400</a>
%H A053109 <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (100, -4500, 120000, -2100000, 25200000, -210000000, 1200000000, -4500000000, 10000000000, -10000000000).
%F A053109 a(n) = 10^n*binomial(n+9, 9);
%F A053109 G.f.: 1/(1-10*x)^10.
%p A053109 seq(coeff(series(1/(1-10*x)^10, x, n+1), x, n), n = 0 .. 15); # _Muniru A Asiru_, Aug 16 2018
%t A053109 CoefficientList[Series[1/(1-10x)^10,{x,0,20}],x] (* or *) Table[10^n Binomial[n+9,9],{n,0,20}] (* _Harvey P. Dale_, May 19 2011 *)
%o A053109 (Sage)[lucas_number2(n, 10, 0)*binomial(n,9)/10 ^9 for n in range(9, 24)] # _Zerinvary Lajos_, Mar 13 2009
%o A053109 (PARI) vector(30,n,n--; 10^n*binomial(n+9, 9)) \\ _G. C. Greubel_, Aug 16 2018
%o A053109 (Magma) [10^n*Binomial(n+9, 9): n in [0..30]]; // _G. C. Greubel_, Aug 16 2018
%o A053109 (GAP) List([0..15],n->10^n*Binomial(n+9,9)); # _Muniru A Asiru_, Aug 16 2018
%K A053109 easy,nonn
%O A053109 0,2
%A A053109 _Wolfdieter Lang_