login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A292928 G.f. A(x) satisfies: A( x^2*A(x) - A(x)^4 ) = x^3. 3
1, 1, 4, 21, 136, 941, 6862, 51998, 405256, 3228208, 26167124, 215135798, 1789732224, 15037735467, 127429439672, 1087804527493, 9345903237508, 80751170130654, 701224835836174, 6116663059682404, 53570252214591940, 470886419343198751, 4152853930912625384, 36735754728365394280, 325861321839388361170, 2897885772356354420332 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Paul D. Hanna, Table of n, a(n) for n = 1..520

FORMULA

a(n) ~ c * d^n / n^(3/2), where d = 9.4477112726509666047269249019968778065... and c = 0.01614622962039842631454... - Vaclav Kotesovec, Oct 10 2017

EXAMPLE

G.f.: A(x) = x + x^2 + 4*x^3 + 21*x^4 + 136*x^5 + 941*x^6 + 6862*x^7 + 51998*x^8 + 405256*x^9 + 3228208*x^10 + 26167124*x^11 + 215135798*x^12 + 1789732224*x^13 + 15037735467*x^14 + 127429439672*x^15 + 1087804527493*x^16 +...

such that A( x^2*A(x) - A(x)^4 ) = x^3.

RELATED SERIES.

x^2*A(x) - A(x)^4 = x^3 - x^6 - 2*x^9 - 6*x^12 - 32*x^15 - 143*x^18 - 718*x^21 - 3866*x^24 - 21054*x^27 - 118409*x^30 +...

Let B(x) be the series reversion of A(x), so that B(A(x)) = x, then

B(x) = x - x^2 - 2*x^3 - 6*x^4 - 32*x^5 - 143*x^6 - 718*x^7 - 3866*x^8 - 21054*x^9 - 118409*x^10 - 679560*x^11 - 3955972*x^12 - 23343650*x^13 - 139235773*x^14 - 838057508*x^15 - 5084422207*x^16 +...

then x^2*A(x) - A(x)^4 = B(x^3).

PROG

(PARI) {a(n) = my(A=[1, 1]); for(i=1, n, A=concat(A, 0); F=x*Ser(A); A[#A] = -Vec(subst(F, x, x^2*F - F^4))[#A] ); polcoeff(A, n)}

for(n=1, 40, print1(a(n), ", "))

CROSSREFS

Cf. A265940, A268039, A272463, A292927.

Sequence in context: A195440 A001909 A205077 * A209881 A052852 A288869

Adjacent sequences:  A292925 A292926 A292927 * A292929 A292930 A292931

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 26 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)