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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A307955 G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n * ((1+x)^(5*n) - A(x))^(n+1), where A(0) = 0. 4
1, 9, 46, 344, 3586, 39676, 490036, 6669184, 97419116, 1519635734, 25170406452, 439941245653, 8081132624095, 155483518553143, 3124130586316551, 65389133324807724, 1422540686845941509, 32103883123046977644, 750278496443387818395, 18128963984900687497993, 452255024819251695443556, 11632687351726270908152086, 308130679955484625602559961, 8395760218678197725930082459 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..24.

FORMULA

G.f. A(x) satisfies:

(1) 1 = Sum_{n>=0} x^n * ((1+x)^(5*n) - A(x))^(n+1).

(2) 1 + x = Sum_{n>=0} x^n * (1+x)^(5*n*(n-1)) / (1 + x*(1+x)^(5*n)*A(x))^(n+1).

(3) 1 = Sum_{n>=0} x^n * (1-x)^(10*n+2) / ((1-x)^(5*n+1) - x*A(x/(1-x)))^(n+1).

(4) 1 = Sum_{n>=0} x^n * (1 - (1-x)^(5*n-5) * A(x/(1-x)))^n / (1-x)^(5*n^2-4*n-1)).

EXAMPLE

G.f.: A(x) = x + 9*x^2 + 46*x^3 + 344*x^4 + 3586*x^5 + 39676*x^6 + 490036*x^7 + 6669184*x^8 + 97419116*x^9 + 1519635734*x^10 + 25170406452*x^11 + ...

such that

1 = (1 - A(x)) + x*((1+x)^5 - A(x))^2 + x^2*((1+x)^10 - A(x))^3 + x^3*((1+x)^15 - A(x))^4 + x^4*((1+x)^20 - A(x))^5 + x^5*((1+x)^25 - A(x))^6 + x^6*((1+x)^30 - A(x))^7 + x^7*((1+x)^35 - A(x))^8 + ...

also

1 + x = 1/(1 + x*A(x)) + x/(1 + x*(1+x)^5*A(x))^2 + x^2*(1+x)^10/(1 + x*(1+x)^10*A(x))^3 + x^3*(1+x)^30/(1 + x*(1+x)^15*A(x))^4 + x^4*(1+x)^60/(1 + x*(1+x)^20*A(x))^5 + x^5*(1+x)^100/(1 + x*(1+x)^25*A(x))^6 + ...

PROG

(PARI) {a(n) = my(A=[1]); for(i=1, n-1, A = concat(A, 0); A[#A] = polcoeff( sum(m=0, #A, x^m*((1+x +x*O(x^#A))^(5*m) - x*Ser(A))^(m+1) ), #A); ); A[n]}

for(n=1, 30, print1(a(n), ", ")) \\ shifted by Georg Fischer, Jun 22 2022

CROSSREFS

Cf. A307940, A307952, A307953, A307954.

Sequence in context: A250722 A250776 A054140 * A110675 A265805 A274270

Adjacent sequences: A307952 A307953 A307954 * A307956 A307957 A307958

KEYWORD

nonn

AUTHOR

Paul D. Hanna, May 07 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 November 29 02:32 EST 2022. Contains 358421 sequences. (Running on oeis4.)