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%I #17 Sep 08 2022 08:45:35
%S 0,4,24,250,3096,40834,554664,7647250,106237176,1481554114,
%T 20701400904,289537131250,4051542498456,56707753666594,
%U 793811662272744,11112685048647250,155572843119354936
%N E.g.f. Sum_{d|M} (exp(d*x)-1)/d, M=14.
%H Vincenzo Librandi, <a href="/A141013/b141013.txt">Table of n, a(n) for n = 0..800</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (24, -163, 336, -196).
%F From _R. J. Mathar_, Mar 05 2010: (Start)
%F a(n) = sum_{d|14} d^(n-1) = 1+2^(n-1)+7^(n-1)+14^(n-1).
%F a(n)= 24*a(n-1) -163*a(n-2) +336*a(n-3) -196*a(n-4), n>4.
%F G.f: -2*x*(-2+36*x-163*x^2+168*x^3)/((x-1)*(14*x-1)*(2*x-1)*(7*x-1)).
%F (End)
%F a(n) = A000051(n-1)*A034491(n-1). - _R. J. Mathar_, May 26 2016
%p A141013 := proc(n) local d; add(d^(n-1),d=numtheory[divisors](14)) ; end proc: seq(A141013(n),n=1..20) ; # _R. J. Mathar_, Mar 05 2010
%t CoefficientList[Series[- 2 x (-2 + 36 x - 163 x^2 + 168 x^3)/((x-1) (14*x-1) (2*x-1) (7*x-1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 12 2012 *)
%o (Magma) [0] cat [1+2^(n-1)+7^(n-1)+14^(n-1): n in [1..20]]; // _Vincenzo Librandi_, Dec 12 2012
%Y Cf. A141012 (M=13), A141014 (M=15).
%K nonn,easy
%O 0,2
%A _R. J. Mathar_, Jul 11 2008
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