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%I #16 Mar 30 2022 06:34:45
%S 59049,3486784401,576650390625,16679880978201,205891132094649,
%T 1531578985264449,8140406085191601,34050628916015625,
%U 119042423827613001,362033331456891249,984930291881790849,2446194060654759801,5631351470947265625,12157665459056928801
%N a(n) = (6n+3)^10.
%H Vincenzo Librandi, <a href="/A016954/b016954.txt">Table of n, a(n) for n = 0..2000</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 _Wesley Ivan Hurt_, Aug 22 2016: (Start)
%F G.f.: 59049*(1 + 59038*x + 9116141*x^2 + 178300904*x^3 + 906923282*x^4 + 1527092468*x^5 + 906923282*x^6 + 178300904*x^7 + 9116141*x^8 + 59038*x^9 + x^10)/(1-x)^11.
%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) for n>10.
%F a(n) = A008454(A016945(n)). (End)
%F From _Amiram Eldar_, Mar 30 2022: (Start)
%F a(n) = A016946(n)^5 = A016949(n)^2.
%F a(n) = 3^10*A016762(n).
%F Sum_{n>=0} 1/a(n) = 31*Pi^10/171421608960. (End)
%p A016954:=n->(6*n+3)^10: seq(A016954(n), n=0..20); # _Wesley Ivan Hurt_, Aug 22 2016
%t (6 Range[0, 20] + 3)^10 (* _Wesley Ivan Hurt_, Aug 22 2016 *)
%o (Magma) [(6*n+3)^10: n in [0..20]]; // _Vincenzo Librandi_, May 06 2011
%Y Cf. A008454, A016762, A016945, A016946, A016947, A016948, A016949, A016950, A016951, A016952, A016953.
%Y Subsequence of A008454.
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_
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