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 A279845 #6 Jan 06 2017 06:19:19
%S A279845 1,1,7,87,1577,37921,1143991,41734167,1793837945,89100737537,
%T A279845 5038278258759,320488252355991,22712229678267017,1778818548078114337,
%U A279845 152926844472960316055,14348332105800041202903,1461880180517958608890585,161034066043430013259095681,19105043857756090069661974951,2432865068875486088572762200535,331511875063241457659846364208233,48205214775404458968179455649349921,7461345443274460130807423699070922103
%N A279845 E.g.f. satisfies: A(x - Integral 2*A(x) dx) = x - Integral A(x) dx.
%F A279845 E.g.f. A(x) satisfies:
%F A279845 (1) A(x - Integral 2*A(x) dx) = x - Integral A(x) dx.
%F A279845 (2) A(x) = x + G( 2*A(x) - x ), where G(x) = Integral A(x) dx.
%F A279845 (3) A(x) = x/2 + 1/2 * Series_Reversion(x - Integral 2*A(x) dx).
%F A279845 (4) A( 2*A(x) - x ) = (A'(x) - 1)/(2*A'(x) - 1).
%F A279845 (5) A'(x - Integral 2*A(x) dx) = (1 - A(x))/(1 - 2*A(x)).
%F A279845 a(n) = Sum_{k=0..n-1} A277410(n,k) * 2^k.
%e A279845 E.g.f.: A(x) = x + x^2/2! + 7*x^3/3! + 87*x^4/4! + 1577*x^5/5! + 37921*x^6/6! + 1143991*x^7/7! + 41734167*x^8/8! + 1793837945*x^9/9! + 89100737537*x^10/10! + 5038278258759*x^11/11! + 320488252355991*x^12/12! + 22712229678267017*x^13/13! + 1778818548078114337*x^14/14! + 152926844472960316055*x^15/15! +...
%o A279845 (PARI) /* A(x) = x + (p+q)*G((p*A(x) + q*x)/(p+q)) ; G(x) = Integral A(x) dx: */
%o A279845 {a(n, p=2, q=-1) = my(A=x, G); for(i=1, n, G = intformal(A +x*O(x^n)); A = x + (p+q)*subst(G, x, (p*A + q*x)/(p+q)) +x*O(x^n)); n!*polcoeff(A, n)}
%o A279845 for(n=1, 30, print1(a(n, 2, -1), ", "))
%o A279845 (PARI) /* A(x - Integral p*A(x) dx) = x + Integral q*A(x) dx: */
%o A279845 {a(n, p=2, q=-1) = my(A=[1], F=x); for(i=1, n, A=concat(A, 0); F=x*Ser(A); G=intformal(F); A[#A] = -polcoeff(subst(F, x, x - p*G) - q*G, #A) ); n!*A[n]}
%o A279845 for(n=1, 30, print1(a(n, 2, -1), ", "))
%o A279845 (PARI) /* Informal code to generate the first N terms: */
%o A279845 {N=20; p=2; q=-1; A=x; for(i=1, N, G=intformal(A +x*O(x^N)); A = x + (p+q)*subst(G, x, (p*A + q*x)/(p+q))); Vec(serlaplace(A))}
%Y A279845 Cf. A277410, A210949, A277403, A279843, A279844, A280570, A280571, A280572, A280573, A280574, A280575.
%K A279845 nonn
%O A279845 1,3
%A A279845 _Paul D. Hanna_, Jan 05 2017