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A294328 a(n) = ((9*n + 8)*10^n - 8)/81.

%I A294328 #17 Sep 17 2023 18:53:44
%S A294328 0,2,32,432,5432,65432,765432,8765432,98765432,1098765432,12098765432,
%T A294328 132098765432,1432098765432,15432098765432,165432098765432,
%U A294328 1765432098765432,18765432098765432,198765432098765432,2098765432098765432,22098765432098765432
%N A294328 a(n) = ((9*n + 8)*10^n - 8)/81.
%H A294328 Colin Barker, <a href="/A294328/b294328.txt">Table of n, a(n) for n = 0..900</a>
%H A294328 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (21,-120,100).
%F A294328 a(n) = (1/9) * A294327(n) = (1/8) * A294329(n).
%F A294328 From _Colin Barker_, Oct 28 2017: (Start)
%F A294328 G.f.: 2*x*(1 - 5*x) / ((1 - x)*(1 - 10*x)^2).
%F A294328 a(n) = 21*a(n-1) - 120*a(n-2) + 100*a(n-3) for n>2.
%F A294328 (End)
%e A294328 Curious multiplications:
%e A294328          2 * 8 =       16;
%e A294328         32 * 8 =      256;
%e A294328        432 * 8 =     3456;
%e A294328       5432 * 8 =    43456;
%e A294328      65432 * 8 =   523456;
%e A294328     765432 * 8 =  6123456;
%e A294328    8765432 * 8 = 70123456.
%e A294328          2 * 9 =       18;
%e A294328         32 * 9 =      288;
%e A294328        432 * 9 =     3888;
%e A294328       5432 * 9 =    48888;
%e A294328      65432 * 9 =   588888;
%e A294328     765432 * 9 =  6888888;
%e A294328    8765432 * 9 = 78888888.
%t A294328 LinearRecurrence[{21,-120,100},{0,2,32},20] (* _Harvey P. Dale_, Sep 17 2023 *)
%o A294328 (PARI) concat(0, Vec(2*x*(1 - 5*x) / ((1 - x)*(1 - 10*x)^2) + O(x^30))) \\ _Colin Barker_, Oct 28 2017
%Y A294328 Cf. A294327, A294329.
%K A294328 nonn,easy
%O A294328 0,2
%A A294328 _Seiichi Manyama_, Oct 28 2017