cp's OEIS Frontend

A088578 a(n) = n*x^n + (n-1)*x^(n-1) + . . . + x + 1 for x=2.

%I A088578 #25 Sep 08 2022 08:45:12
%S A088578 1,3,11,35,99,259,643,1539,3587,8195,18435,40963,90115,196611,425987,
%T A088578 917507,1966083,4194307,8912899,18874371,39845891,83886083,176160771,
%U A088578 369098755,771751939,1610612739,3355443203,6979321859,14495514627,30064771075,62277025795
%N A088578 a(n) = n*x^n + (n-1)*x^(n-1) + . . . + x + 1 for x=2.
%C A088578 For x=1 this is A000124.
%C A088578 Equals row sums of triangle A144332. Left border of A144332 = A000124. - _Gary W. Adamson_, Sep 18 2008
%H A088578 Colin Barker, <a href="/A088578/b088578.txt">Table of n, a(n) for n = 0..1000</a>
%H A088578 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,4).
%F A088578 a(n) = (n-1) * 2^(n+1) + 3.
%F A088578 a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). - _Colin Barker_, Apr 02 2012
%F A088578 G.f.: (1-2*x+4*x^2)/((1-x)*(1-2*x)^2). - _Colin Barker_, Apr 02 2012
%e A088578 Sum of reciprocals = 1.469480896985753544533086291..
%t A088578 LinearRecurrence[{5,-8,4},{1,3,11},40] (* _Harvey P. Dale_, Dec 22 2013 *)
%t A088578 Table[(n - 1) 2^(n + 1) + 3, {n, 0, 30}] (* _Vincenzo Librandi_, Jun 14 2015 *)
%o A088578 (PARI) trajpolypn(n1,k) = { s=0; for(x1=1,n1, y1 = polypn2(k,x1); print1(y1","); s+=1.0/y1; ); print(); print(s) } polypn2(n,p) = { x=n; y=1; for(m=1,p, y=y+m*x^m; ); return(y) }
%o A088578 (PARI) Vec((1-2*x+4*x^2)/((1-x)*(1-2*x)^2) + O(x^50)) \\ _Colin Barker_, Jun 13 2015
%o A088578 (Magma) I:=[1,3,11]; [n le 3 select I[n] else 5*Self(n-1)-8*Self(n-2)+4*Self(n-3): n in [1..35]]; // _Vincenzo Librandi_, Jun 14 2015
%Y A088578 Cf. A000124.
%Y A088578 Cf. A144332.
%K A088578 nonn,easy
%O A088578 0,2
%A A088578 _Cino Hilliard_, Nov 20 2003