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A182304 G.f. satisfies: A(x) = x + d/dx A(x)^3/3. 4
1, 1, 4, 25, 200, 1890, 20248, 240069, 3102000, 43226590, 644778520, 10237504810, 172274940656, 3061868388100, 57310884482160, 1126953452418765, 23230411494361920, 501015558669312390, 11285603304699928600, 265077311648541268030, 6482435029801210815280 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
G.f. satisfies: A(x) = x + A'(x)*A(x)^2.
a(n) ~ c * n! * n^3, where c = 0.0147556981601927885048672335828437... - Vaclav Kotesovec, Feb 22 2014
G.f.: A(x) = Series_Reversion(x/F(x)) where F(x) = 1 + x*F(x)^3/(F(x) - x*F'(x)) is the g.f. of A245118. - Paul D. Hanna, Jul 27 2014
EXAMPLE
G.f.: A(x) = x + x^2 + 4*x^3 + 25*x^4 + 200*x^5 + 1890*x^6 + 20248*x^7 +...
Related expansions.
A'(x) = 1 + 2*x + 12*x^2 + 100*x^3 + 1000*x^4 + 11340*x^5 + 141736*x^6 +...
A(x)^2 = x^2 + 2*x^3 + 9*x^4 + 58*x^5 + 466*x^6 + 4380*x^7 + 46501*x^8 +...
A(x)^3 = x^3 + 3*x^4 + 15*x^5 + 100*x^6 + 810*x^7 + 7593*x^8 + 80023*x^9 +...
d/dx A(x)^3 = 3*x^2 + 12*x^3 + 75*x^4 + 600*x^5 + 5670*x^6 + 60744*x^7 +...
PROG
(PARI) {a(n)=local(A=x+x^2+x*O(x^n)); for(i=1, n, A=x+deriv(A^3/3+O(x^31))); polcoeff(A, n)}
for(n=1, 25, print1(a(n), ", "))
(PARI) /* From g.f. F(x) of A245118 (Paul D. Hanna, Jul 27 2014): */
{a(n)=local(F=1+x); for(i=1, n, F = 1 + x*F^3/(F - x*F' +x*O(x^n))); polcoeff(serreverse(x/F), n)}
for(n=1, 25, print1(a(n), ", "))
CROSSREFS
Sequence in context: A284859 A144647 A215505 * A060910 A195260 A254796
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 23 2012
STATUS
approved

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Last modified June 22 00:43 EDT 2024. Contains 373561 sequences. (Running on oeis4.)