|
%I #19 Dec 31 2023 10:22:47
%S 1024,9765625,1073741824,25937424601,289254654976,2015993900449,
%T 10240000000000,41426511213649,141167095653376,420707233300201,
%U 1125899906842624,2758547353515625,6278211847988224,13422659310152401,27197360938418176,52599132235830049
%N a(n) = (3*n + 2)^10.
%H T. D. Noe, <a href="/A016798/b016798.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
%F From _Harvey P. Dale_, Nov 28 2014: (Start)
%F G.f.: -(1/((x-1)^11))(x^10+1048565*x^9+270940968*x^8+6950443776*x^7+ 43221615834*x^6+86805830970*x^5+61387794480*x^4+14663204952*x^3+ 966376269*x^2+9754361*x+1024).
%F a(n) = 59049*n^10 + 393660*n^9 + 1180980*n^8 + 2099520*n^7 + 2449440*n^6 + 1959552*n^5 + 1088640*n^4 + 414720*n^3 + 103680*n^2 + 15360*n + 1024. [corrected by _Amiram Eldar_, Mar 31 2022] (End)
%F From _Amiram Eldar_, Mar 31 2022: (Start)
%F a(n) = A016789(n)^10 = A016790(n)^5 = A016793(n)^2.
%F Sum_{n>=0} 1/a(n) = PolyGamma(9, 2/3)/21427701120. (End)
%F a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11). - _Wesley Ivan Hurt_, Dec 31 2023
%t (3*Range[0,20]+2)^10 (* _Harvey P. Dale_, Nov 28 2014 *)
%Y Cf. A016789, A016790, A016791, A016792, A016793, A016794, A016795.
%Y Subsequence of A008454.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_.
|
