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 A277612 #5 Nov 07 2016 14:54:49
%S A277612 1,4,24,224,2880,47104,935424,21853184,587089920,17829167104,
%T A277612 603915485184,22571950997504,922735222456320,40954197741666304,
%U A277612 1961183862263906304,100787274348058640384,5532701353887903252480,323102311113161602760704,20000832981651983154806784,1308180577070098190616756224,90146906116103034082689024000,6527896185206802934447948693504
%N A277612 E.g.f. satisfies: A(x - sin(x)^2) = x + sin(x)^2.
%F A277612 G.f. A(x) also satisfies:
%F A277612 (1) A(x) = 1+x - cos(A(x) + x).
%F A277612 (2) A(x) = x + 2 * sin( (A(x) + x)/2 )^2.
%F A277612 (3) A(x) = -x + 2 * Series_Reversion(x - sin(x)^2).
%F A277612 a(n) = 2 * A143134(n) for n>1.
%e A277612 E.g.f.: A(x) = x + 4*x^2/2! + 24*x^3/3! + 224*x^4/4! + 2880*x^5/5! + 47104*x^6/6! + 935424*x^7/7! + 21853184*x^8/8! + 587089920*x^9/9! + 17829167104*x^10/10! +...
%e A277612 such that A(x - sin(x)^2) = x + sin(x)^2.
%e A277612 RELATED SERIES.
%e A277612 A(x - sin(x)^2) = x + 2*x^2/2! - 8*x^4/4! + 32*x^6/6! - 128*x^8/8! + 512*x^10/10! - 2048*x^12/12! +...
%e A277612 which equals x + sin(x)^2.
%e A277612 cos(A(x) + x) = 1 - 4*x^2/2! - 24*x^3/3! - 224*x^4/4! - 2880*x^5/5! - 47104*x^6/6! +...
%e A277612 which equals 1+x - A(x).
%o A277612 (PARI) {a(n) = my(A=x); for(i=1,21,A = subst(x + sin(x +x*O(x^n) )^2,x, serreverse(x - sin(x +x*O(x^n) )^2))); n!*polcoeff(A,n)}
%o A277612 for(n=1,25,print1(a(n),", "))
%o A277612 (PARI) {a(n) = my(A=x); for(i=0,n, A = 1+x - cos(A + x +x*O(x^n))); n!*polcoeff(A,n)}
%o A277612 for(n=1,25,print1(a(n),", "))
%Y A277612 Cf. A143134.
%K A277612 nonn
%O A277612 1,2
%A A277612 _Paul D. Hanna_, Nov 06 2016