%I #10 Oct 19 2017 03:44:25

%S 4715040,8463840,1122749669280,2015496399840,267373851637578960,

%T 479974343542849680,63672943775553479639280,114302050117965712710960,

%U 15163202176330482896520455040,27220118818712616412771202880,3610995292612020914167620625112640

%N Octagonal numbers (A000567) that are the sum of fifteen consecutive octagonal numbers.

%H Colin Barker, <a href="/A258132/b258132.txt">Table of n, a(n) for n = 1..370</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,238142,-238142,-1,1).

%F G.f.: -240*x*(7*x^4 +4*x^3 -449376*x^2 +15620*x +19646)/((x-1)*(x^2 -488*x +1)*(x^2 +488*x +1)).

%e 4715040 is in the sequence because Oct(1254) = 4715040 = 300833 + 302736 + 304645 + 306560 + 308481 + 310408 + 312341 + 314280 + 316225 + 318176 + 320133 + 322096 + 324065 + 326040 + 328021 = Oct(317) + ... + Oct(331).

%t CoefficientList[Series[-240*x*(7*x^4 +4*x^3 -449376*x^2 +15620*x +19646)/((x-1)*(x^2 -488*x +1)*(x^2 +488*x +1)), {x, 0, 50}], x] (* _G. C. Greubel_, Oct 18 2017 *)

%o (PARI) Vec(-240*x*(7*x^4 +4*x^3 -449376*x^2 +15620*x +19646)/((x-1)*(x^2 -488*x +1)*(x^2 +488*x +1)) + O('x^20))

%Y Cf. A000567, A258128, A258129, A258130, A258131.

%K nonn,easy

%O 1,1

%A _Colin Barker_, May 21 2015