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A081189 7th binomial transform of (1,0,1,0,1,...), A059841.

%I A081189 #37 Sep 08 2022 08:45:09
%S A081189 1,7,50,364,2696,20272,154400,1188544,9228416,72147712,567104000,
%T A081189 4476365824,35448129536,281408253952,2238205337600,17827278536704,
%U A081189 142148043309056,1134363236564992,9057979233075200,72362273907933184
%N A081189 7th binomial transform of (1,0,1,0,1,...), A059841.
%C A081189 Binomial transform of A081188.
%C A081189 a(n) is the number of functions f:{1,2,...,n}->{1,2,3,4,5,6,7,8} with an even number of elements mapped to 1. - _Geoffrey Critzer_, Dec 30 2012
%C A081189 For the alternative formulation in terms of words of length n over an alphabet of eight letters with a chosen letter appearing an even number of times see a comment in A007582, also for the crossrefs, for the 1- to 11- letter word cases. - _Wolfdieter Lang_, Jul 17 2017
%H A081189 Vincenzo Librandi, <a href="/A081189/b081189.txt">Table of n, a(n) for n = 0..200</a>
%H A081189 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-48).
%F A081189 a(n) = 14*a(n-1) - 48*a(n-2) with n > 1, a(0)=1, a(1)=7.
%F A081189 G.f.: (1-7*x)/((1-6*x)*(1-8*x)).
%F A081189 E.g.f. exp(7*x)*cosh(x).
%F A081189 a(n) = 6^n/2 + 8^n/2.
%F A081189 a(n) = 6*a(n-1) + 8^(n-1).
%t A081189 nn=20;Range[0,nn]!CoefficientList[Series[Exp[7x]Cosh[x],{x,0,nn}],x]  (* _Geoffrey Critzer_, Dec 30 2012 *)
%t A081189 LinearRecurrence[{14, -48}, {1, 7}, 20] (* Or *)
%t A081189 CoefficientList[Series[(1 - 7 x)/(1 - 14 x + 48 x^2), {x, 0, 19}], x] (* _Robert G. Wilson v_, Jan 02 2013 *)
%o A081189 (Magma) [6^n/2 + 8^n/2: n in [0..20]]; // _Vincenzo Librandi_, Aug 07 2013
%Y A081189 Cf. A007582, A081190.
%K A081189 nonn,easy
%O A081189 0,2
%A A081189 _Paul Barry_, Mar 11 2003