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A226067
G.f. satisfies: A(x) = 1 + x*( d/dx x*A(x)^8 )^(1/4).
2
1, 1, 4, 21, 132, 960, 7944, 74335, 786932, 9456258, 129313528, 2010416336, 35343702312, 696506363140, 15229800217104, 365825127164457, 9567409932676756, 270380073725933200, 8204936841573636120, 265952811211238746138, 9166927690425432138872, 334710118083817942361700
OFFSET
0,3
LINKS
FORMULA
a(n) ~ c * 2^n * n! / n^(5/2), where c = 4.72771780666962546492... - Vaclav Kotesovec, Nov 21 2017
EXAMPLE
G.f.: A(x) = 1 + x + 4*x^2 + 21*x^3 + 132*x^4 + 960*x^5 + 7944*x^6 +...
Related expansions:
A(x)^8 = 1 + 8*x + 60*x^2 + 448*x^3 + 3422*x^4 + 27168*x^5 + 226960*x^6 +...
d/dx x*A(x)^8 = 1 + 16*x + 180*x^2 + 1792*x^3 + 17110*x^4 + 163008*x^5 +...
(d/dx x*A(x)^8)^(1/4) = 1 + 4*x + 21*x^2 + 132*x^3 + 960*x^4 + 7944*x^5 +...
PROG
(PARI) {a(n)=local(A=1+x); for(i=1, n, A=1+x*deriv(x*A^8+x*O(x^n))^(1/4)); polcoeff(A, n)}
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
Cf. A213192.
Sequence in context: A332851 A303563 A284816 * A104982 A306335 A195440
KEYWORD
nonn
AUTHOR
Paul D. Hanna, May 24 2013
STATUS
approved