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A143924 E.g.f. A(x) satisfies: A(x) = 1 + x*exp(Integral A(x)^4 dx). 3
1, 1, 2, 15, 132, 1545, 22590, 392595, 7923720, 182140245, 4696277250, 134227563855, 4211901994860, 143942600513985, 5321725064741190, 211627606517556075, 9007288512919672080, 408543101848039590285 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
Compare definition of e.g.f. A(x) to the trivial statement:
if F(x) = 1/(1-x) then F(x) = 1 + x*exp(Integral F(x) dx).
Here Integral F(x) dx does not include the constant of integration.
Limit n->infinity (a(n)/n!)^(1/n) = 2.792845... - Vaclav Kotesovec, Feb 28 2014
LINKS
FORMULA
E.g.f. derivative: A'(x) = [1 + x*A(x)^4]*(A(x) - 1)/x.
EXAMPLE
E.g.f. A(x) = 1+ x + 2*x^2/2! + 12*x^3/3! + 88*x^4/4! + 860*x^5/5! +...
A(x)^4 = 1 + 4*x + 20*x^2/2! + 144*x^3/3! +1384*x^4/4! +16400*x^5/5!+...
Let L(x) = Integral A(x)^4 dx where A(x) = 1 + x*exp(L(x)), then
L(x) = x + 4*x^2/2! + 20*x^3/3! + 144*x^4/4! + 1384*x^5/5! +...
exp(L(x)) = 1 + x + 5*x^2/2! + 33*x^3/3! + 297*x^4/4! + 3385*x^5/5! +...
PROG
(PARI) {a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=1+x*exp(intformal(A^4))); n!*polcoeff(A, n)}
CROSSREFS
Sequence in context: A132182 A365151 A140306 * A217483 A214043 A347993
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Sep 06 2008
STATUS
approved

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Last modified February 24 07:07 EST 2024. Contains 370294 sequences. (Running on oeis4.)