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A353098 a(1) = 6; for n>1, a(n) = 7 * a(n-1) + 7 - n.

%I A353098 #25 May 29 2023 07:13:06
%S A353098 6,47,333,2334,16340,114381,800667,5604668,39232674,274628715,
%T A353098 1922401001,13456807002,94197649008,659383543049,4615684801335,
%U A353098 32309793609336,226168555265342,1583179886857383,11082259208001669,77575814456011670,543030701192081676
%N A353098 a(1) = 6; for n>1, a(n) = 7 * a(n-1) + 7 - n.
%H A353098 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-15,7).
%F A353098 G.f.: x * (6 - 7 * x)/((1 - x)^2 * (1 - 7 * x)).
%F A353098 a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3).
%F A353098 a(n) = 5 * A014830(n) + n.
%F A353098 a(n) = (5*7^(n+1) + 6*n - 35)/36.
%F A353098 a(n) = Sum_{k=0..n-1} (7 - n + k)*7^k.
%F A353098 E.g.f.: exp(x)*(35*(exp(6*x) - 1) + 6*x)/36. - _Stefano Spezia_, May 29 2023
%t A353098 LinearRecurrence[{9, -15, 7}, {6, 47, 333}, 21] (* _Amiram Eldar_, Apr 23 2022 *)
%o A353098 (PARI) my(N=30, x='x+O('x^N)); Vec(x*(6-7*x)/((1-x)^2*(1-7*x)))
%o A353098 (PARI) a(n) = (5*7^(n+1)+6*n-35)/36;
%o A353098 (PARI) b(n, k) = sum(j=0, n-1, (k-n+j)*k^j);
%o A353098 a(n) = b(n, 7);
%Y A353098 Cf. A064617, A353094, A353095, A353096, A353097, A353099, A353100.
%Y A353098 Cf. A014830.
%K A353098 nonn,easy
%O A353098 1,1
%A A353098 _Seiichi Manyama_, Apr 23 2022