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%I #36 Sep 08 2022 08:45:49
%S 1,15,210,2940,41160,576240,8067360,112943040,1581202560,22136835840,
%T 309915701760,4338819824640,60743477544960,850408685629440,
%U 11905721598812160,166680102383370240,2333521433367183360,32669300067140567040,457370200939967938560,6403182813159551139840
%N Expansion of g.f.: (1+x)/(1-14*x).
%C For n>=1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,...,14} with no two adjacent letters identical. -_Milan Janjic_, Jan 31 2015
%H Vincenzo Librandi, <a href="/A170734/b170734.txt">Table of n, a(n) for n = 0..800</a>
%H M. Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Janjic/janjic63.html">On Linear Recurrence Equations Arising from Compositions of Positive Integers</a>, J. Int. Seq. 18 (2015) # 15.4.7.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (14).
%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*15^k. - _Philippe Deléham_, Dec 04 2009
%F a(0) = 1; for n>0, a(n) = 15*14^(n-1). - _Vincenzo Librandi_, Dec 05 2009
%F a(0) = 1, a(1) = 15, a(n) = 14*a(n-1). - _Vincenzo Librandi_, Dec 10 2012
%F E.g.f.: (15*exp(14*x) -1)/14. - _G. C. Greubel_, Sep 24 2019
%p k:=15; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 24 2019
%t Join[{1}, 15*14^Range[0, 25]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 11 2011 *)
%t CoefficientList[Series[(1+x)/(1-14x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 10 2012 *)
%o (PARI) vector(26, n, k=15; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Sep 24 2019
%o (Magma) k:=15; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Sep 24 2019
%o (Sage) k=15; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 24 2019
%o (GAP) k:=15;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Sep 24 2019
%Y Cf. A003945, A003954, A097805, A170733.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 04 2009
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