VOOZH about

URL: https://oeis.org/A236955

⇱ A236955 - OEIS

login
A236955
E.g.f. satisfies: A'(x) = A(x)^7 * A(-x)^2 with A(0) = 1.
6
1, 1, 5, 61, 905, 20473, 508685, 16761013, 585178385, 25302198769, 1138789420565, 60931744739629, 3358493791987865, 214135163725140457, 13970561744501181725, 1033867628277644584357, 77925569710983386849825, 6564469233905978976791521, 561328952232987425817545765
OFFSET
0,3
LINKS
FORMULA
E.g.f.: 1/(1 - 4*Series_Reversion( Integral (1 - 16*x^2)^(1/2) dx ))^(1/4).
EXAMPLE
E.g.f.: A(x) = 1 + x + 5*x^2/2! + 61*x^3/3! + 905*x^4/4! + 20473*x^5/5! + ...
Related series.
A(x)^7 = 1 + 7*x + 77*x^2/2! + 1267*x^3/3! + 26873*x^4/4! + 712831*x^5/5! + ...
Note that 1 - 1/A(x)^4 is an odd function:
1 - 1/A(x)^4 = 4*x + 64*x^3/3! + 13312*x^5/5! + 8077312*x^7/7! + 9796059136*x^9/9! + ...
where Series_Reversion((1 - 1/A(x)^4)/4) = Integral (1-16*x^2)^(1/2) dx.
MATHEMATICA
With[{nmax = 40}, CoefficientList[1/(1 - 4*InverseSeries[Series[ Integrate[ (1 - 16*x^2)^(1/2) , x], {x, 0, nmax}], x])^(1/4), x]*Range[0, nmax]!] (* G. C. Greubel, Nov 20 2017 *)
PROG
(PARI) {a(n)=local(A=1); for(i=0, n, A=1+intformal(A^7*subst(A^2, x, -x) +x*O(x^n) )); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
(PARI) {a(n)=local(A=1); A=1/(1-4*serreverse(intformal((1-16*x^2 +x*O(x^n))^(2/4))))^(1/4); n!*polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Apr 09 2014
STATUS
approved