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A215116
G.f. satisfies: A(x) = x + 3*x^2 + x*A(A(A(A(x)))).
5
1, 4, 16, 256, 4864, 111616, 2983936, 89743360, 2970861568, 106768629760, 4125849419776, 170207219286016, 7454572671926272, 345078981839552512, 16822127738969128960, 860944587541763325952, 46137178395559050870784, 2582843669636660403896320, 150735442996358913332346880
OFFSET
1,2
COMMENTS
The (1/4)-iteration of the g.f. equals an integer series (A215117).
EXAMPLE
G.f.: A(x) = x + 4*x^2 + 16*x^3 + 256*x^4 + 4864*x^5 + 111616*x^6 + 2983936*x^7 +...
where
A(A(A(A(x)))) = x + 16*x^2 + 256*x^3 + 4864*x^4 + 111616*x^5 + 2983936*x^6 +...
Related expansions.
Let D(D(D(D(x)))) = A(x), then D(x) is an integer series where:
D(x) = x + x^2 + x^3 + 49*x^4 + 721*x^5 + 17281*x^6 + 452065*x^7 +...
where the coefficients of D(x) are congruent to 1 modulo 48.
PROG
(PARI) {a(n)=local(A=x+4*x^2); for(i=1, n, A=x+3*x^2+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), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Aug 03 2012
STATUS
approved