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A064749 a(n) = n*11^n + 1.

%I A064749 #25 May 04 2025 04:47:14
%S A064749 1,12,243,3994,58565,805256,10629367,136410198,1714871049,21221529220,
%T A064749 259374246011,3138428376722,37661140520653,448795257871104,
%U A064749 5316497670165375,62658722541234766,735195677817154577,8592599484487994108,100078511642860166659,1162022718519876379530
%N A064749 a(n) = n*11^n + 1.
%H A064749 Vincenzo Librandi, <a href="/A064749/b064749.txt">Table of n, a(n) for n = 0..900</a>
%H A064749 Paul Leyland, <a href="https://web.archive.org/web/20120204131613/http://www.leyland.vispa.com/numth/factorization/cullen_woodall/cw.htm">Factors of Cullen and Woodall numbers</a>.
%H A064749 Paul Leyland, <a href="https://web.archive.org/web/20120204131629/http://www.leyland.vispa.com/numth/factorization/cullen_woodall/gcw.htm">Generalized Cullen and Woodall numbers</a>.
%H A064749 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (23,-143,121).
%F A064749 a(n) = A064757(n) + 2 for n>=1. - _Georg Fischer_, Feb 19 2021
%F A064749 G.f.: -(110*x^2-11*x+1)/((x-1)*(11*x-1)^2). - _Alois P. Heinz_, Feb 19 2021
%F A064749 From _Elmo R. Oliveira_, May 03 2025: (Start)
%F A064749 E.g.f.: exp(x)*(1 + 11*x*exp(10*x)).
%F A064749 a(n) = 23*a(n-1) - 143*a(n-2) + 121*a(n-3). (End)
%p A064749 k:= 11; f:= gfun:-rectoproc({-1 - (k-1)*n + k*n*a(n-1) - (n-1)*a(n) = 0, a(0) = 1, a(1) = k+1}, a(n), remember): map(f, [$0..20]); # _Georg Fischer_, Feb 19 2021
%o A064749 (Magma) [n*11^n+1: n in [0..20]]; // _Vincenzo Librandi_, Sep 16 2011
%Y A064749 For a(n)=n*k^n+1: A000012 (k=0), A000027(n+1) (k=1), A002064 (k=2), A050914 (k=3), A050915 (k=4), A050916 (k=5), A050917 (k=6), A050919 (k=7), A064746 (k=8), A064747 (k=9), A064748 (k=10), this sequence (k=11), A064750 (k=12).
%Y A064749 Cf. A064757.
%K A064749 nonn,easy
%O A064749 0,2
%A A064749 _N. J. A. Sloane_, Oct 19 2001