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A242749 G.f. satisfies: A(x) = G(x/A(x)) such that A(x*G(x)) = G(x) = Sum_{n>=0} (n+1)^(n+1)*x^n.

%I A242749 #5 May 21 2014 22:46:36
%S A242749 1,4,11,60,611,8632,151538,3132140,73883667,1949844168,56785116742,
%T A242749 1806695366616,62314198956510,2315470815127792,92214156916779444,
%U A242749 3918743752606940812,177018691811732542595,8471087431826716955880,428141645771934036086942,22791557465710675500959688
%N A242749 G.f. satisfies: A(x) = G(x/A(x)) such that A(x*G(x)) = G(x) = Sum_{n>=0} (n+1)^(n+1)*x^n.
%F A242749 G.f. satisfies: [x^n] A(x)^(n+1) = (n+1)^(n+2).
%F A242749 G.f.: A(x) = x/Series_Reversion(x*G(x)) where G(x) = Sum_{n>=0} (n+1)^(n+1)*x^n.
%e A242749 G.f.: A(x) = 1 + 4*x + 11*x^2 + 60*x^3 + 611*x^4 + 8632*x^5 + 151538*x^6 +...
%e A242749 such that A(x*G(x)) = G(x) where:
%e A242749 G(x) = 1 + 4*x + 27*x^2 + 256*x^3 + 3125*x^4 +...+ (n+1)^(n+1)*x^n +...
%e A242749 also, A(x) = G(x/A(x)):
%e A242749 A(x) = 1 + 4*x/A(x) + 27*x^2/A(x)^2 + 256*x^3/A(x)^3 + 3125*x^4/A(x)^4 +...+ (n+1)^(n+1)*x^n/A(x)^n +...
%e A242749 If we form a table of coefficients of x^k in A(x)^n like so:
%e A242749 [1,  4,  11,   60,   611,   8632,  151538,   3132140, ...];
%e A242749 [1,  8,  38,  208,  1823,  23472,  389174,   7739808, ...];
%e A242749 [1, 12,  81,  508,  4164,  48852,  759407,  14463624, ...];
%e A242749 [1, 16, 140, 1024,  8418,  91920, 1335712,  24248640, ...];
%e A242749 [1, 20, 215, 1820, 15625, 163664, 2232620,  38498580, ...];
%e A242749 [1, 24, 306, 2960, 27081, 279936, 3623894,  59297664, ...];
%e A242749 [1, 28, 413, 4508, 44338, 462476, 5764801,  89716400, ...];
%e A242749 [1, 32, 536, 6528, 69204, 739936, 9018480, 134217728, ...]; ...
%e A242749 then the main diagonal forms the sequence A007778:
%e A242749 [1, 8, 81, 1024, 15625, 279936, 5764801, 134217728, ..., (n+1)^(n+2), ...].
%o A242749 (PARI) {a(n)=polcoeff(x/serreverse(x*sum(m=0, n+1, (m+1)^(m+1)*x^m)+x^2*O(x^n)), n)}
%o A242749 for(n=0,20,print1(a(n),", "))
%Y A242749 Cf. A180749, A007778.
%K A242749 nonn
%O A242749 0,2
%A A242749 _Paul D. Hanna_, May 21 2014