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 A085528 #32 Sep 08 2022 08:45:11
%S A085528 1,9,125,2401,59049,1771561,62748517,2562890625,118587876497,
%T A085528 6131066257801,350277500542221,21914624432020321,1490116119384765625,
%U A085528 109418989131512359209,8629188747598184440949,727423121747185263828481,65273511648264442971824673
%N A085528 a(n) = (2*n+1)^(n+1).
%C A085528 a(n) is the number of polynomials of degree at most n with integer coefficients all having absolute value <= n.
%C A085528 a(n-1) is the number of nodes in the canonical automaton for the affine Weyl group of type D_n. - _Tom Edgar_, May 12 2016
%D A085528 Anders Björner and Francesco Brenti, Combinatorics of Coxeter groups. Graduate Texts in Mathematics, 231. Springer, New York, 2005.
%H A085528 Vincenzo Librandi, <a href="/A085528/b085528.txt">Table of n, a(n) for n = 0..100</a>
%F A085528 From _Peter Bala_, Aug 06 2012: (Start)
%F A085528 E.g.f.: d/dx{(2*x/T(2*x))^(1/2)*1/(1 - T(2*x))} = 1 + 9*x + 125*x^2/2! + ..., where T(x) is the tree function sum {n >= 1} n^(n-1)*x^n/n! of A000169.
%F A085528 For r = 0, 1, 2, ... the e.g.f. for the sequence (2*n+1)^(n+r) can be expressed in terms of the function U(z) = sum {n >= 0} (2*n+1)^(n-1)*z^(2*n+1)/(2^n*n!). See A214406 for details. In the present case, r = 1, and the resulting e.g.f. is 1/z*U(z)*(1 + U(z)^2 )/(1 - U(z)^2)^3 taken at z = sqrt(2*x).
%F A085528 (End)
%F A085528 Sum_{n>=0} (-1)^n/a(n) = A253299. - _Amiram Eldar_, Jun 25 2021
%p A085528 seq((2*n+1)^(n+1), n=0..20); # _G. C. Greubel_, Sep 03 2019
%t A085528 Table[(2*n+1)^(n+1), {n,0,20}] (* _Vladimir Joseph Stephan Orlovsky_, Sep 05 2009, modified by _G. C. Greubel_, Sep 03 2019 *)
%o A085528 (Magma) [(2*n+1)^(n+1): n in [0..20]]; // _Vincenzo Librandi_, May 04 2011
%o A085528 (PARI) vector(20, n, (2*n-1)^n) \\ _G. C. Greubel_, Sep 03 2019
%o A085528 (Sage) [(2*n+1)^(n+1) for n in (0..20)] # _G. C. Greubel_, Sep 03 2019
%o A085528 (GAP) List([0..20], n-> (2*n+1)^(n+1)); # _G. C. Greubel_, Sep 03 2019
%Y A085528 Cf. A000169, A085527, A099753, A214406, A253299.
%K A085528 nonn,easy
%O A085528 0,2
%A A085528 _N. J. A. Sloane_, Jul 05 2003