|
%I #18 May 18 2023 13:20:49
%S 0,4,24,260,3528,51332,762744,11406980,170939688,2563287812,
%T 38445332184,576660215300,8649804864648,129746582562692,
%U 1946196290656824,29192932133689220,437893920912786408
%N E.g.f. Sum_{d|M} (exp(d*x)-1)/d, M=15.
%H Vincenzo Librandi, <a href="/A141014/b141014.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, -158, 360, -225).
%F a(n) = sum_{d|15} d^(n-1) = 1+3^(n-1)+5^(n-1)+15^(n-1). G.f.: -4*x*(-1+18*x-79*x^2+90*x^3)/((x-1) * (15*x-1) * (3*x-1) * (5*x-1)). a(n) = 24*a(n-1) -158*a(n-2) +360*a(n-3) -225*a(n-4). - _R. J. Mathar_, Mar 05 2010
%F a(n) = A034472(n-1)*A034474(n-1). - _R. J. Mathar_, May 26 2016
%p A141014 := proc(n) local d; add(d^(n-1),d=numtheory[divisors](15)) ; end proc: seq(A141014(n),n=1..20) ; # _R. J. Mathar_, Mar 05 2010
%t CoefficientList[Series[-4 x (-1 + 18 x - 79 x^2 + 90 x^3)/((x-1) (15 x-1) (3 x-1) (5 x-1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 13 2012 *)
%t LinearRecurrence[{24,-158,360,-225},{0,4,24,260,3528},20] (* _Harvey P. Dale_, May 18 2023 *)
%o (Magma) [0] cat [1+3^(n-1)+5^(n-1)+15^(n-1): n in [1..20]]; // _Vincenzo Librandi_, Dec 13 2012
%K nonn,easy
%O 0,2
%A _R. J. Mathar_, Jul 11 2008
|
