%I #16 Jun 13 2015 00:55:22

%S 55,220,1210,7942,57838,450670,3682030,31153342,270739678,2403012910,

%T 21693441550,198578979742,1838853136318,17193665419150,

%U 162090976108270,1538867288166142,14698448516729758,141129617123665390,1361277292619082190

%N a(n) = 9*2^n + 7*4^n + 3*8^n + 8*3^n + 2*9^n + 6*5^n + 5*6^n + 4*7^n + 10^n + 10.

%C This is the sequence of tenth terms of "second partial sums of m-th powers".

%H Colin Barker, <a href="/A254148/b254148.txt">Table of n, a(n) for n = 0..999</a>

%H Luciano Ancora, <a href="/A254148/a254148.pdf">Demonstration of formulas</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (55,-1320,18150,-157773,902055,-3416930,8409500,-12753576,10628640,-3628800).

%F G.f.: -(80627040*x^9 -184920912*x^8 +175484892*x^7 -91478420*x^6 +29111445*x^5 -5902743*x^4 +766458*x^3 -61710*x^2 +2805*x -55) / ((x -1)*(2*x -1)*(3*x -1)*(4*x -1)*(5*x -1)*(6*x -1)*(7*x -1)*(8*x -1)*(9*x -1)*(10*x -1)). - _Colin Barker_, Jan 28 2015

%o (PARI) vector(30, n, n--; 9*2^n + 7*4^n + 3*8^n + 8*3^n + 2*9^n + 6*5^n + 5*6^n + 4*7^n + 10^n + 10) \\ _Colin Barker_, Jan 28 2015

%Y Cf. A052548, A254028, A254030, A254031, A254144, A254145, A254146, A254147.

%K nonn,easy

%O 0,1

%A _Luciano Ancora_, Jan 28 2015