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URL: https://oeis.org/A247029

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A247029
G.f. A(x) satisfies A(x) = A(x)^4 - 9*x.
6
1, 3, -18, 180, -2187, 29484, -424116, 6377292, -99034650, 1576075644, -25569752274, 421325812440, -7031733125508, 118620405322020, -2019349799669160, 34647126360607440, -598525520999144643, 10401492640172342940, -181721630178565389900, 3189811189331825319492
OFFSET
0,2
LINKS
FORMULA
G.f.: x / Series_Reversion( x*(1 + 9*x)^(1/3) ).
Recurrence: (n-2)*(n-1)*n*a(n) = -216*(2*n - 5)*(4*n - 13)*(4*n - 7)*a(n-3). - Vaclav Kotesovec, Nov 18 2017
a(n) ~ -(-1)^n * 2^(8*n/3 - 13/6) * 3^n / (sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Nov 18 2017
G.f. A(x) satisfies A(x) = 1/A(-x/A(x)^5). - Seiichi Manyama, Jun 20 2025
EXAMPLE
G.f.: A(x) = 1 + 3*x - 18*x^2 + 180*x^3 - 2187*x^4 + 29484*x^5 - 424116*x^6 +...
where
A(x)^4 = 1 + 12*x - 18*x^2 + 180*x^3 - 2187*x^4 + 29484*x^5 - 424116*x^6 +...
MATHEMATICA
FullSimplify[Table[-(-1)^n * 3^(2*n-1) * 4^(n-1) * Gamma[n/3 + 1/6] * Gamma[2*n/3 - 1/6] / (Pi * Gamma[n + 1]), {n, 0, 20}]] (* Vaclav Kotesovec, Nov 18 2017 *)
PROG
(PARI) {a(n)=polcoeff(x/serreverse(x*(1+9*x +x^2*O(x^n))^(1/3)), n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
sign
AUTHOR
Paul D. Hanna, Sep 09 2014
STATUS
approved