login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A323320 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( (1+x)^n - 19*x*A(x) )^n * 9^n / 10^(n+1). 9
1, 189, 136341, 165866949, 274513563621, 564389814803319, 1373687351977035681, 3844220718032111632869, 12130905677234774784280281, 42569255610714760893622565829, 164374338314267349285576891426201, 692583662656534583930262265650693159, 3162450027762781275258550249673787013761, 15558457725978409248029649314240444710279749, 82059484588450416190385956503916602281112899421 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..14.

FORMULA

G.f. A(x) satisfies the following identities.

(1) 1 = Sum_{n>=0} ( (1+x)^n - 19*x*A(x) )^n * 9^n / 10^(n+1).

(2) 1 = Sum_{n>=0} (1+x)^(n^2) * 9^n / (10 + 171*x*A(x)*(1+x)^n)^(n+1).

EXAMPLE

G.f.: A(x) = 1 + 189*x + 136341*x^2 + 165866949*x^3 + 274513563621*x^4 + 564389814803319*x^5 + 1373687351977035681*x^6 + 3844220718032111632869*x^7 + ...

such that

1 = 1/10 + ((1+x) - 19*x*A(x))*9/10^2 + ((1+x)^2 - 19*x*A(x))^2*9^2/10^3 + ((1+x)^3 - 19*x*A(x))^3*9^3/10^4 + ((1+x)^4 - 19*x*A(x))^4*9^4/10^5 + ...

Also,

1 = 1/(10 + 171*x*A(x)) + (1+x)*9/(10 + 171*x*A(x)*(1+x))^2 + (1+x)^4*9^2/(10 + 171*x*A(x)*(1+x)^2)^3 + (1+x)^9*9^3/(10 + 171*x*A(x)*(1+x)^3)^4 + ...

PROG

(PARI) \p120

{A=vector(1); A[1]=1; for(i=1, 20, A = concat(A, 0);

A[#A] = round( Vec( sum(n=0, 2400, ( (1+x +x*O(x^#A))^n - 19*x*Ser(A) )^n * 9^n/10^(n+1)*1.)/171 ) )[#A+1]); A}

CROSSREFS

Cf. A301435, A303288, A323314, A323315, A323316, A323317, A323318, A323319, A323321.

Sequence in context: A286791 A076012 A092136 * A352759 A259166 A156741

Adjacent sequences:  A323317 A323318 A323319 * A323321 A323322 A323323

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 10 2019

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 1 11:38 EDT 2022. Contains 357147 sequences. (Running on oeis4.)