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A215118
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G.f. satisfies: A(x) = x + 4*x^2 + x*A(A(A(A(A(x))))).
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4
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1, 5, 25, 625, 18125, 628125, 25390625, 1158515625, 58308203125, 3190470703125, 187941103515625, 11832996337890625, 791834056298828125, 56063448811767578125, 4184231129351806640625, 328154000925299072265625, 26970505516268341064453125, 2317475342690856231689453125
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OFFSET
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1,2
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COMMENTS
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The (1/5)-iteration of the g.f. equals an integer series (A215119).
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LINKS
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Table of n, a(n) for n=1..18.
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EXAMPLE
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G.f.: A(x) = x + 5*x^2 + 25*x^3 + 625*x^4 + 18125*x^5 + 628125*x^6 +...
where
A(A(A(A(x)))) = x + 25*x^2 + 625*x^3 + 18125*x^4 + 628125*x^5 +...
Related expansions.
Let E(E(E(E(E(x))))) = A(x), then E(x) is an integer series where:
E(x) = x + x^2 + x^3 + 101*x^4 + 2301*x^5 + 82601*x^6 + 3287001*x^7 +...
where the coefficients of E(x) are congruent to 1 modulo 100.
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PROG
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(PARI) {a(n)=local(A=x+4*x^2); for(i=1, n, A=x+4*x^2+x*subst(A, x, subst(A, x, subst(A, x, subst(A, x, A+x*O(x^n)))))); polcoeff(A, n)}
for(n=1, 31, print1(a(n), ", "))
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CROSSREFS
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Cf. A215119, A213010, A215114, A215116.
Sequence in context: A175852 A030995 A067270 * A218150 A176594 A274463
Adjacent sequences: A215115 A215116 A215117 * A215119 A215120 A215121
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna, Aug 03 2012
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STATUS
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approved
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