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 A266487 #7 Mar 19 2025 15:04:31
%S A266487 1,1,-3,31,-559,14541,-496811,21081859,-1070585055,63366015673,
%T A266487 -4285932328819,326248732427751,-27610580638457807,
%U A266487 2572239828612623365,-261621661000490429211,28849626308051995285771,-3428690784657696770593471,436924188109882619766249201,-59432725217403244945921112675,8595527924368773785463788378287,-1317123285394547040368548520041839,213171869078193696050387803319525821,-36338236299957647745418230431675850763,6507698606647750492700809995200106342675,-1221579456277487714539848255959245396739999
%N A266487 E.g.f.: Limit_{N->oo} [ Sum_{n>=0} (N - n)^(2*n) * (x/N)^n/n! ]^(1/N).
%C A266487 Compare to: Limit_{N->oo} [ Sum_{n>=0} (N + n)^n * x^n/n! ]^(1/N) = Sum_{n>=0} (n+1)^(n-1) * x^n/n!.
%e A266487 E.g.f.: A(x) = 1 + x - 3*x^2/2! + 31*x^3/3! - 559*x^4/4! + 14541*x^5/5! - 496811*x^6/6! + 21081859*x^7/7! - 1070585055*x^8/8! + 63366015673*x^9/9! - 4285932328819*x^10/10! +...
%e A266487 where A(x) equals the limit, as N -> oo, of the series
%e A266487 [1 + (N-1)^2*(x/N) + (N-2)^4*(x/N)^2/2! + (N-3)^6*(x/N)^3/3! + (N-4)^8*(x/N)^4/4! + (N-5)^10*(x/N)^5/5! + (N-6)^12*(x/N)^6/6! +...]^(1/N).
%o A266487 (PARI) /* Informal listing of terms 0..30 */
%o A266487 \p300
%o A266487 H(n) = sum(k=0,32, (n - k)^(2*k) * x^k/k! +O(x^32))
%o A266487 Vec( round( serlaplace( subst(H(10^100)^(1/10^100),x,x/10^100) )*1.) )
%Y A266487 Cf. A266481, A266482, A266483, A266484, A266485, A266486.
%K A266487 sign
%O A266487 0,3
%A A266487 _Paul D. Hanna_, Dec 30 2015