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A353100 a(1) = 8; for n>1, a(n) = 9 * a(n-1) + 9 - n.

%I A353100 #28 May 29 2023 07:13:14
%S A353100 8,79,717,6458,58126,523137,4708235,42374116,381367044,3432303395,
%T A353100 30890730553,278016574974,2502149174762,22519342572853,
%U A353100 202674083155671,1824066748401032,16416600735609280,147749406620483511,1329744659584351589,11967701936259164290
%N A353100 a(1) = 8; for n>1, a(n) = 9 * a(n-1) + 9 - n.
%H A353100 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-19,9).
%F A353100 G.f.: x * (8 - 9 * x)/((1 - x)^2 * (1 - 9 * x)).
%F A353100 a(n) = 11*a(n-1) - 19*a(n-2) + 9*a(n-3).
%F A353100 a(n) = 7 * A014832(n) + n.
%F A353100 a(n) = (7*9^(n+1) + 8*n - 63)/64.
%F A353100 a(n) = Sum_{k=0..n-1} (9 - n + k)*9^k.
%F A353100 E.g.f.: exp(x)*(63*(exp(8*x) - 1) + 8*x)/64. - _Stefano Spezia_, May 29 2023
%t A353100 LinearRecurrence[{11, -19, 9}, {8, 79, 717}, 20] (* _Amiram Eldar_, Apr 23 2022 *)
%o A353100 (PARI) my(N=30, x='x+O('x^N)); Vec(x*(8-9*x)/((1-x)^2*(1-9*x)))
%o A353100 (PARI) a(n) = (7*9^(n+1)+8*n-63)/64;
%o A353100 (PARI) b(n, k) = sum(j=0, n-1, (k-n+j)*k^j);
%o A353100 a(n) = b(n, 9);
%Y A353100 Cf. A064617, A353094, A353095, A353096, A353097, A353098, A353099.
%Y A353100 Cf. A014832.
%K A353100 nonn,easy
%O A353100 1,1
%A A353100 _Seiichi Manyama_, Apr 23 2022