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 A132683 #15 Mar 14 2021 18:44:19
%S A132683 1,3,15,165,4845,435897,131115985,138432467745,525783425977953,
%T A132683 7271150092378906305,368539102493388126164865,
%U A132683 68777035446753808820521420545,47450879627176629761462147774626305
%N A132683 a(n) = binomial(2^n + n, n).
%H A132683 G. C. Greubel, <a href="/A132683/b132683.txt">Table of n, a(n) for n = 0..50</a>
%F A132683 a(n) = [x^n] 1/(1-x)^(2^n + 1).
%F A132683 G.f.: Sum_{n>=0} (-log(1 - 2^n*x))^n / ((1 - 2^n*x)*n!). - _Paul D. Hanna_, Feb 25 2009
%F A132683 a(n) ~ 2^(n^2) / n!. - _Vaclav Kotesovec_, Jul 02 2016
%e A132683 From _Paul D. Hanna_, Feb 25 2009: (Start)
%e A132683 G.f.: A(x) = 1 + 3*x + 15*x^2 + 165*x^3 + 4845*x^4 + 435897*x^5 + ...
%e A132683 A(x) = 1/(1-x) - log(1-2x)/(1-2x) + log(1-4x)^2/((1-4x)*2!) - log(1-8x)^3/((1-8x)*3!) +- ... (End)
%p A132683 A132683:= n-> binomial(2^n +n,n); seq(A132683(n), n=0..20); # _G. C. Greubel_, Mar 14 2021
%t A132683 Table[Binomial[2^n+n, n], {n, 0, 15}] (* _Vaclav Kotesovec_, Jul 02 2016 *)
%o A132683 (PARI) a(n)=binomial(2^n+n,n)
%o A132683 (PARI) {a(n)=polcoeff(sum(m=0,n,(-log(1-2^m*x))^m/((1-2^m*x +x*O(x^n))*m!)),n)} \\ _Paul D. Hanna_, Feb 25 2009
%o A132683 (Sage) [binomial(2^n +n, n) for n in (0..20)] # _G. C. Greubel_, Mar 14 2021
%o A132683 (Magma) [Binomial(2^n +n, n): n in [0..20]]; // _G. C. Greubel_, Mar 14 2021
%Y A132683 Sequences of the form binomial(2^n +p*n +q, n): A136556 (0,-1), A014070 (0,0), A136505 (0,1), A136506 (0,2), A060690 (1,-1), this sequence (1,0), A132684 (1,1), A132685 (2,0), A132686 (2,1), A132687 (3,-1), A132688 (3,0), A132689 (3,1).
%Y A132683 Cf. A136555.
%Y A132683 Cf. A066384. - _Paul D. Hanna_, Feb 25 2009
%K A132683 nonn
%O A132683 0,2
%A A132683 _Paul D. Hanna_, Aug 26 2007