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%I #29 Sep 30 2022 14:37:12
%S 1,5,45,405,3645,32805,295245,2657205,23914845,215233605,1937102445,
%T 17433922005,156905298045,1412147682405,12709329141645,
%U 114383962274805,1029455660473245,9265100944259205,83385908498332845,750473176484995605,6754258588364960445,60788327295284644005
%N Third column of triangle A067402.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (9).
%F a(n) = A067402(n+2, 2).
%F a(n) = 5*9^(n-1) for n>=1, a(0) = 1.
%F G.f.: (1-4*x)/(1-9*x).
%F E.g.f.: (4 + 5*exp(9*x))/9. - _Stefano Spezia_, Sep 30 2022
%p A067403:=n->5*9^(n-1): 1,seq(A067403(n), n=1..30); # _Wesley Ivan Hurt_, Apr 09 2017
%t Join[{1},NestList[9#&,5,30]] (* or *) CoefficientList[Series[ (1-4x)/ (1-9x),{x,0,30}],x] (* _Harvey P. Dale_, Apr 26 2011 *)
%o (PARI) Vec((1-4*x)/(1-9*x) + O(x^30)) \\ _Michel Marcus_, Apr 09 2017
%Y Cf. A002001 (second column), A067404 (fourth column), A001019 (powers of 9).
%Y Cf. A067402.
%K nonn,easy
%O 0,2
%A _Wolfdieter Lang_, Jan 25 2002
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