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a(n) = n*x^n + (n-1)*x^(n-1) + . . . + x + 1 for x=5.
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%I #15 Jul 15 2020 13:24:34

%S 1,6,56,431,2931,18556,112306,659181,3784181,21362306,119018556,

%T 656127931,3585815431,19454956056,104904174806,562667846681,

%U 3004074096681,15974044799806,84638595581056,447034835815431,2354383468627931,12367963790893556,64820051193237306

%N a(n) = n*x^n + (n-1)*x^(n-1) + . . . + x + 1 for x=5.

%H Colin Barker, <a href="/A277975/b277975.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-35,25).

%F G.f.: (1 - 5*x + 25*x^2)/((1 - x)*(1 - 5*x)^2).

%F a(n) = 11*a(n-1) - 35*a(n-2) + 25*a(n-3) for n>2.

%F a(n) = (21 - 5^(1+n) + 4*5^(1+n)*n)/16.

%e a(3) = 3*5^3 + (3-1)*5^(3-1) + 5 + 1 = 431.

%t LinearRecurrence[{11,-35,25},{1,6,56},30] (* _Harvey P. Dale_, Jul 15 2020 *)

%o (PARI) Vec((1-5*x+25*x^2)/((1-x)*(1-5*x)^2) + O(x^30)) \\ _Colin Barker_, Nov 07 2016

%Y Cf. A088581, A088582.

%K nonn,easy

%O 0,2

%A _Colin Barker_, Nov 07 2016