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%I #21 Jun 29 2023 18:15:14
%S 1,10,99,972,9477,91854,885735,8503056,81310473,774840978,7360989291,
%T 69735688020,659002251789,6213449802582,58462914051567,
%U 549043018919064,5147278302366225,48178524910147866,450283905890997363
%N 9th binomial transform of (1,1,0,0,0,0,0,...).
%C Main diagonal of array defined by m(0,j) = j; m(i,0) = i and m(i,j) = m(i-1,j) + 8*m(i-1,j-1). - _Benoit Cloitre_, Jun 13 2003
%H Vincenzo Librandi, <a href="/A081109/b081109.txt">Table of n, a(n) for n = 0..300</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18, -81).
%F a(n) = 18*a(n-1) - 81*a(n-2), a(0) = 1, a(1) = 10.
%F a(n) = (n + 9)*9^(n-1).
%F G.f.: (1 - 8*x)/(1 - 9*x)^2.
%F E.g.f.: exp(9*x)*(1 + x). - _Stefano Spezia_, Mar 04 2023
%t CoefficientList[Series[(1 - 8 x) / (1 - 9 x)^2, {x, 0, 30}], x] (* _Vincenzo Librandi_, Aug 06 2013 *)
%o (Magma) [(n+9)*9^(n-1): n in [0..25]]; // _Vincenzo Librandi_, Aug 06 2013
%Y Cf. A081108, A081122, A006234.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Mar 07 2003
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