This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A303653 G.f. A(x) satisfies: 1 = Sum_{n>=0} ( 3*(1+x)^n - A(x) )^n / 3^(n+1). 2
 1, 15, 291, 20868, 2501535, 406641390, 82021892979, 19576367780568, 5370958558206975, 1661471768423203359, 571522497313691705223, 216322544080204799422227, 89344723486622904627485286, 39989870323587920736747152457, 19285197574525200774860259575856, 9970552400727667627167081347333058, 5502200681071110455003310691040648913 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Paul D. Hanna, Table of n, a(n) for n = 0..50 FORMULA G.f.: 1 = Sum_{n>=0} 3^n * (1+x)^(n^2) / (3 + (1+x)^n * A(x))^(n+1). EXAMPLE G.f.: A(x) = 1 + 15*x + 291*x^2 + 20868*x^3 + 2501535*x^4 + 406641390*x^5 + 82021892979*x^6 + 19576367780568*x^7 + 5370958558206975*x^8 + ... such that 1 = 1/3  +  (3*(1+x) - A(x))/3^2  +  (3*(1+x)^2 - A(x))^2/3^3  +  (3*(1+x)^3 - A(x))^3/3^4  +  (3*(1+x)^4 - A(x))^4/3^5  +  (3*(1+x)^5 - A(x))^5/3^6 + ... Also, 1 = 1/(3 + A(x))  +  3*(1+x)/(3 + (1+x)*A(x))^2  +  3^2*(1+x)^4/(3 + (1+x)^2*A(x))^3  +  3^3*(1+x)^9/(3 + (1+x)^3*A(x))^4  +  3^4*(1+x)^16/(3 + (1+x)^4*A(x))^5  +  3^5*(1+x)^25/(3 + (1+x)^5*A(x))^6  + ... CROSSREFS Cf. A301436. Sequence in context: A069405 A125055 A160397 * A185809 A231792 A201029 Adjacent sequences:  A303650 A303651 A303652 * A303654 A303655 A303656 KEYWORD nonn AUTHOR Paul D. Hanna, Apr 28 2018 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.

Last modified December 8 18:37 EST 2019. Contains 329865 sequences. (Running on oeis4.)