This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A060416 #32 May 06 2025 09:34:36
%S A060416 1,3,31,191,1023,5119,24575,114687,524287,2359295,10485759,46137343,
%T A060416 201326591,872415231,3758096383,16106127359,68719476735,292057776127,
%U A060416 1236950581247,5222680231935,21990232555519,92358976733183,387028092977151,1618481116086271,6755399441055743
%N A060416 a(n) = n*4^n - 1, with a(0) = 1.
%H A060416 Harry J. Smith, <a href="/A060416/b060416.txt">Table of n, a(n) for n = 0..200</a>
%H A060416 Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm">Factors of Cullen and Woodall numbers</a>.
%H A060416 Paul Leyland, <a href="http://www.leyland.vispa.com/numth/factorization/cullen_woodall/gcw.htm">Generalized Cullen and Woodall numbers</a>.
%H A060416 Amelia Carolina Sparavigna, <a href="https://doi.org/10.5281/zenodo.3471358">The groupoids of Mersenne, Fermat, Cullen, Woodall and other Numbers and their representations by means of integer sequences</a>, Politecnico di Torino, Italy (2019), [math.NT].
%H A060416 Amelia Carolina Sparavigna, <a href="https://doi.org/10.18483/ijSci.2188">Some Groupoids and their Representations by Means of Integer Sequences</a>, International Journal of Sciences (2019) Vol. 8, No. 10.
%H A060416 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,-24,16).
%F A060416 G.f.: (1 - 6*x + 28*x^2 - 32*x^3)/((1 - x)*(1 - 4*x)^2). - _Colin Barker_, Apr 22 2012
%F A060416 From _Elmo R. Oliveira_, May 05 2025: (Start)
%F A060416 E.g.f.: 2 + exp(x)*(4*x*exp(3*x) - 1).
%F A060416 a(n) = A018215(n) - 1 for n >= 1.
%F A060416 a(n) = 9*a(n-1) - 24*a(n-2) + 16*a(n-3) for n > 3. (End)
%t A060416 CoefficientList[Series[(1 - 6 x + 28 x^2 - 32 x^3)/((1 - x) (1 - 4 x)^2), {x, 0, 21}], x] (* _Michael De Vlieger_, Jan 04 2020 *)
%o A060416 (PARI) a(n) = { abs(n*4^n - 1) } \\ _Harry J. Smith_, Jul 04 2009
%Y A060416 Cf. A003261, A018215.
%K A060416 nonn,easy
%O A060416 0,2
%A A060416 _Jason Earls_, Apr 05 2001