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 A073478 #17 Nov 24 2024 08:34:12
%S A073478 1,1,2,9,44,290,2154,19026,186752,2070792,25119720,334960560,
%T A073478 4824346152,75100568088,1250180063664,22235660291880,419595248663040,
%U A073478 8388866239417920,176823515257447104,3923498370610292544
%N A073478 Expansion of (1+x)^(1/(1-x)).
%H A073478 Vincenzo Librandi, <a href="/A073478/b073478.txt">Table of n, a(n) for n = 0..200</a>
%F A073478 E.g.f.: exp( Sum_{n>=1} x^n * Sum_{k=1..n} -(-1)^k/k ). - _Paul D. Hanna_, Jan 08 2014
%F A073478 E.g.f.: exp( Sum_{n>=1} x^n * ((1-x^n)/(1-x)) / n ). - _Paul D. Hanna_, Nov 24 2024
%F A073478 a(n) ~ (log(2))^(1/4) * exp(2*sqrt(n*log(2)) - n - 1/2) * n^(n-1/4). - _Vaclav Kotesovec_, Apr 21 2014
%e A073478 E.g.f.: (1+x)^(1/(1-x)) = 1 + x + 2*x^2/2! + 9*x^3/3! + 44*x^4/4! + 290*x^5/5! + 2154*x^6/6! + 19026*x^7/7! + 186752*x^8/8! + 2070792*x^9/9! + ...
%e A073478 which may be written as
%e A073478 (1+x)^(1/(1-x)) = exp(x + x^2*(1+x)/2 + x^3*(1+x+x^2)/3 + x^4*(1+x+x^2+x^3)/4 + x^5*(1+x+x^2+x^3+x^4)/5 + ... + x^n*((1-x^n)/(1-x))/n + ...).
%t A073478 CoefficientList[Series[(1+x)^(1/(1-x)), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Apr 21 2014 *)
%o A073478 (PARI) {a(n)=n!*polcoeff((1+x +x*O(x^n))^(1/(1-x)),n)} \\ _Paul D. Hanna_, Jan 08 2014
%o A073478 (PARI) {a(n)=local(A);A=exp(sum(m=1,n,sum(k=1,m,-(-1)^k/k)*x^m)+x*O(x^n)); n!*polcoeff(A,n)} \\ _Paul D. Hanna_, Jan 08 2014
%Y A073478 Cf. A007113, A007120, A087761.
%K A073478 nonn
%O A073478 0,3
%A A073478 _Vladeta Jovovic_, Aug 26 2002
%E A073478 More terms from _Robert G. Wilson v_, Aug 28 2002