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Sum of all numbers that appear when we interpret an ordered subset of [0,1,...,n] containing n as the digits, possibly larger than nine, of a base ten number, with the smallest element being the least significant.
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%I #52 Jul 20 2016 14:24:08

%S 11,253,4257,63085,872861,11569833,148920497,1876301845,23259261861,

%T 284671240513,3448396611737,41419505367405,493973128085261,

%U 5855648668464793,69053522207998977,810643999691917765,9478691806054675061,110443295770481522673

%N Sum of all numbers that appear when we interpret an ordered subset of [0,1,...,n] containing n as the digits, possibly larger than nine, of a base ten number, with the smallest element being the least significant.

%H Colin Barker, <a href="/A274129/b274129.txt">Table of n, a(n) for n = 1..950</a>

%H Marko Riedel, <a href="/A274129/a274129.maple.txt">Maple code to compute sequence by enumeration and from the generating function.</a>

%H Math.Stackexchange.Com, Marko Riedel et al., <a href="http://math.stackexchange.com/questions/1851478/">Decreasing sequence numbers</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (24,-165,242).

%F a(n) = (10/9) * n * 11^n - (11/81) * (11^n-2^n).

%F G.f.: 11 * z * (1-z) / ((1-11z)^2 * (1-2z)).

%F a(n) = 24*a(n-1)-165*a(n-2)+242*a(n-3) for n>3. - _Colin Barker_, Jul 20 2016

%e a(2) = 253 because 210+21+20+2 = 253.

%p A274129 := n -> 10/9*n*11^n - 11/81*(11^n-2^n);

%t CoefficientList[Series[11*x*(1 - x)/((1 - 11*x)^2*(1 - 2*x)), {x, 0, 100} ], x] (* _G. C. Greubel_, Jul 07 2016 *)

%o (PARI) Vec(11*x*(1-x)/((1-11*x)^2*(1-2*x)) + O(x^20)) \\ _Colin Barker_, Jul 20 2016

%K nonn,base,easy

%O 1,1

%A _Marko Riedel_, Jul 07 2016