A016872 - OEIS

%I #12 May 24 2024 14:31:49

%S 1,2176782336,3138428376721,281474976710656,7355827511386641,

%T 95428956661682176,787662783788549761,4738381338321616896,

%U 22563490300366186081,89762301673555234816,309629344375621415601

%N a(n) = (5n+1)^12.

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (13, -78, 286, -715, 1287, -1716, 1716, -1287, 715, -286, 78, -13, 1).

%F G.f.: (1/((-1+x)^13))(-1-2176782323*x-3110130206431*x^2- 240845196835205*x^3- 3940827667784970*x^4- 20862213080713758*x^5- 42580224506082654*x^6- 35676286810866378*x^7- 12088615801745445*x^8- 1498318763749055*x^9- 53023637023891*x^10- 282211432673*x^11- 16777216*x^12). - _Harvey P. Dale_, Aug 26 2021

%F a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13). - _Wesley Ivan Hurt_, May 24 2024

%t (5*Range[0,20]+1)^12 (* or *) LinearRecurrence[{-13,78,-286,715,-1287,1716,-1716,1287,-715,286,-78,13,-1},{1,2176782336,3138428376721,281474976710656,7355827511386641,95428956661682176,787662783788549761,4738381338321616896,22563490300366186081,89762301673555234816,309629344375621415601,951166013805414055936,2654348974297586158321},20] (* _Harvey P. Dale_, Aug 26 2021 *)

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_.