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A234855 E.g.f. satisfies: A(x) = Sum_{n>=0} ( Integral A(x)^n dx )^n.

%I A234855 #18 Jan 03 2014 20:11:53
%S A234855 1,1,3,21,241,3951,85499,2325205,76860673,3014656183,137784836475,
%T A234855 7235668490589,431692029451009,28991550501283359,2174713803535479419,
%U A234855 181001542259074421413,16618721538838243841185,1674634828088234390862727,184352162064651888588105243
%N A234855 E.g.f. satisfies: A(x) = Sum_{n>=0} ( Integral A(x)^n dx )^n.
%H A234855 Paul D. Hanna, <a href="/A234855/b234855.txt">Table of n, a(n) for n = 0..100</a>
%F A234855 E.g.f. satisfies: A'(x) = Sum_{n>=1} n * A(x)^n * ( Integral A(x)^n dx )^(n-1).
%e A234855 E.g.f.: A(x) = 1 + x + 3*x^2/2! + 21*x^3/3! + 241*x^4/4! + 3951*x^5/5! +...
%e A234855 To illustrate how the terms are generated, form a table of coefficients of x^k/k!, k>=0, in (Integral A(x)^n dx)^n for n>=0 like so:
%e A234855 n=0: [1, 0, 0,  0,   0,    0,     0,      0,        0,         0, ...];
%e A234855 n=1: [0, 1, 1,  3,  21,  241,  3951,  85499,  2325205,  76860673, ...];
%e A234855 n=2: [0, 0, 2, 12,  88,  920, 13328, 254744,  6161568, 182632584, ...];
%e A234855 n=3: [0, 0, 0,  6, 108, 1710, 29700, 600642, 14344092, 403670790, ...];
%e A234855 n=4: [0, 0, 0,  0,  24,  960, 28800, 826560, 24665088, 793449216, ...];
%e A234855 n=5: [0, 0, 0,  0,   0,  120,  9000, 462000, 20958000, 922005000, ...];
%e A234855 n=6: [0, 0, 0,  0,   0,    0,   720,  90720,  7378560, 504040320, ...];
%e A234855 n=7: [0, 0, 0,  0,   0,    0,     0,   5040,   987840, 120022560, ...];
%e A234855 n=8: [0, 0, 0,  0,   0,    0,     0,      0,    40320,  11612160, ...];
%e A234855 n=9: [0, 0, 0,  0,   0,    0,     0,      0,        0,    362880, ...]; ...
%e A234855 then the column sums form the terms of this sequence.
%o A234855 (PARI) {a(n)=local(A=1+x);for(i=1,n,A=sum(k=0,30,intformal( (A+x*O(x^n))^k )^k));n!*polcoeff(A,n)}
%o A234855 for(n=0,20,print1(a(n),", "))
%Y A234855 Cf. A232552, A107595.
%K A234855 nonn
%O A234855 0,3
%A A234855 _Paul D. Hanna_, Jan 01 2014