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 A245768 #5 Aug 01 2014 00:45:12
%S A245768 1,1,4,26,224,2337,28088,377144,5544824,88039724,1494960308,
%T A245768 26954440490,513267546824,10279486681982,215822203235952,
%U A245768 4737785187211908,108509135362455192,2588049036893027820,64180886929824389840,1652564046132761428040,44124859215715377422552,1220338620776444854394561
%N A245768 G.f. satisfies: A(x) = 1 + x*A(x)^4 / (A(x) - x*A'(x)).
%F A245768 G.f. A(x) satisfies:
%F A245768 (1) [x^n] A(x)^(n+1) = (n+1) * [x^(n-1)] A(x)^(n+3) for n>=1.
%F A245768 (2) A(x) = x/Series_Reversion(G(x)) where G(x) = x*G(x)^4 + x^2*G(x)^3*G'(x).
%e A245768 G.f.: A(x) = 1 + x + 4*x^2 + 26*x^3 + 224*x^4 + 2337*x^5 + 28088*x^6 +...
%e A245768 The table of coefficients of x^k in A(x)^n begin:
%e A245768 n=1: [1, 1, 4, 26, 224, 2337, 28088, 377144, ...];
%e A245768 n=2: [1, 2, 9, 60, 516, 5330, 63318, 840808, ...];
%e A245768 n=3: [1, 3, 15, 103, 888, 9105, 107050, 1406655, ...];
%e A245768 n=4: [1, 4, 22, 156, 1353, 13804, 160844, 2092748, ...];
%e A245768 n=5: [1, 5, 30, 220, 1925, 19586, 226480, 2919840, ...];
%e A245768 n=6: [1, 6, 39, 296, 2619, 26628, 305979, 3911688, ...];
%e A245768 n=7: [1, 7, 49, 385, 3451, 35126, 401625, 5095392, ...];
%e A245768 n=8: [1, 8, 60, 488, 4438, 45296, 515988, 6501760, ...];
%e A245768 n=9: [1, 9, 72, 606, 5598, 57375, 651948, 8165700, ...];
%e A245768 n=10:[1, 10, 85, 740, 6950, 71622, 812720, 10126640, ...]; ...
%e A245768 in which the diagonals illustrate the relation
%e A245768 [x^n] A(x)^(n+1) = (n+1) * [x^(n-1)] A(x)^(n+3) for n>=1
%e A245768 as follows:
%e A245768 [x^1] A(x)^2 = 2 = 2*[x^0] A(x)^4 = 2*1 ;
%e A245768 [x^2] A(x)^3 = 15 = 3*[x^1] A(x)^5 = 3*5 ;
%e A245768 [x^3] A(x)^4 = 156 = 4*[x^2] A(x)^6 = 4*39 ;
%e A245768 [x^4] A(x)^5 = 1925 = 5*[x^3] A(x)^7 = 5*385 ;
%e A245768 [x^5] A(x)^6 = 26628 = 6*[x^4] A(x)^8 = 6*4438 ;
%e A245768 [x^6] A(x)^7 = 401625 = 7*[x^5] A(x)^9 = 7*57375 ;
%e A245768 [x^7] A(x)^8 = 6501760 = 8*[x^6] A(x)^10 = 8*812720 ; ...
%e A245768 Also, from the above table, we can generate:
%e A245768 [1/1, 2/2, 15/3, 156/4, 1925/5, 26628/6, 401625/7, 812720/8, ...]
%e A245768 = [1, 1, 5, 39, 385, 4438, 57375, 812720, 12428977, 203183595, ...];
%e A245768 the g.f. G(x) of which begins:
%e A245768 G(x) = x + x^2 + 5*x^3 + 39*x^4 + 385*x^5 + 4438*x^6 + 57375*x^7 +...
%e A245768 such that:
%e A245768 G(x) = x*G(x)^4 + x^2*G(x)^3*G'(x) and G(x) = A(G(x)).
%o A245768 (PARI) /* From [x^n] A(x)^(n+1) = (n+1) * [x^(n-1)] A(x)^(n+3): */
%o A245768 {a(n)=local(A=[1, 1]); for(i=2, n, A=concat(A, 0); A[#A]=((#A)*Vec(Ser(A)^(#A+2))[#A-1]-Vec(Ser(A)^(#A))[#A])/(#A)); A[n+1]}
%o A245768 for(n=0,30,print1(a(n),", "))
%o A245768 (PARI) /* From A(x) = 1 + x*A(x)^4 / (A(x) - x*A'(x)): */
%o A245768 {a(n)=local(A=1+x); for(i=1, n, A = 1 + x*A^4/(A - x*A' +x*O(x^n))); polcoeff(A,n)}
%o A245768 for(n=0,30,print1(a(n),", "))
%o A245768 (PARI) /* From A(x) = x/Series_Reversion(G) where G = x*G^4 + x^2*G^3*G': */
%o A245768 {a(n)=local(G=1+x); for(i=1, n, G = 1 + x*G^4 + x^2*G^3*G' +x*O(x^n)); polcoeff(x/serreverse(x*G +x^2*O(x^n)),n)}
%o A245768 for(n=0,30,print1(a(n),", "))
%Y A245768 Cf. A088715, A245118.
%K A245768 nonn
%O A245768 0,3
%A A245768 _Paul D. Hanna_, Aug 01 2014