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From a solution to the Prouhet-Tarry-Escott problem: 3^n + 5^n + 30^n + 57^n + 104^n + 116^n + 186^n + 198^n + 245^n + 272^n + 297^n + 299^n.
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%I #12 Jan 05 2023 15:17:52

%S 12,1812,413874,104854098,27893252694,7632971084682,2127510153712374,

%T 600674464913818938,171205557239739747654,49150278329342053633482,

%U 14189870202126851375980374,4115100811187433413293653978,1197749131382044008056854855014

%N From a solution to the Prouhet-Tarry-Escott problem: 3^n + 5^n + 30^n + 57^n + 104^n + 116^n + 186^n + 198^n + 245^n + 272^n + 297^n + 299^n.

%C Agrees with A049405 up to n=11.

%D R. K. Guy, Unsolved Problems in the Theory of Numbers, Section D1.

%D Posting by Chen Shuwen (jmchen(AT)pub.jiangmen.gd.cn) to Number Theory List, Sep 09, 1999.

%H <a href="http://euler.free.fr/eslp/k1to11.htm">More info (1)</a>

%H <a href="http://euler.free.fr/eslp/k246810.htm">More info (2)</a>

%H <a href="http://euler.free.fr/eslp/eslp.htm">More info (3)</a>

%H <a href="http://euler.free.fr/eslp/status.htm">More info (4)</a>

%H <a href="http://euler.free.fr/eslp/TarryPrb.htm">More info (5)</a>

%e 12 + 1812*x + 413874*x^2 + 104854098*x^3 + 27893252694*x^4 + ...

%t Table[Total[{3,5,30,57,104,116,186,198,245,272,297,299}^n],{n,0,15}] (* _Harvey P. Dale_, Jan 05 2023 *)

%o (PARI) {a(n) = if( n < 0, 0, 3^n + 5^n + 30^n + 57^n + 104^n + 116^n + 186^n + 198^n + 245^n + 272^n + 297^n + 299^n)} /* _Michael Somos_, Mar 26 2012 */

%Y Cf. A049405.

%K nonn

%O 0,1

%A _Michael Somos_, Sep 09 1999