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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A277041 Limit of the coefficient of x^(3^m + n) in B(x)^(n+1)/(n+1) as m grows, where B(x) = Sum_{k>=0} x^(3^k). 4
 1, 1, 1, 2, 5, 11, 51, 246, 897, 13526, 115631, 614681, 8739556, 89877217, 596072842 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS The expansion of A(x/(1+x))/(1+x) appears to be a power series in x^3. LINKS FORMULA a(n) = A277040(n)/(n+1). Equals the binomial transform of A277043. EXAMPLE G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 11*x^5 + 51*x^6 + 246*x^7 + 897*x^8 + 13526*x^9 + 115631*x^10 + 614681*x^11 + 8739556*x^12 + 89877217*x^13 + 596072842*x^14 +... RELATED SERIES. A(x/G(x)) = G(x) = x/Series_Reversion[x*A(x)], where G(x) = 1 + x + x^3 + 27*x^6 + 10666*x^9 + 6174792*x^12 +...+ A277042(n)*x^n +... and G(x) appears to continue with powers of x^3 only. The inverse binomial transform forms the g.f. of A277043: A(x/(1+x))/(1+x) = 1 + x^3 + 30*x^6 + 10921*x^9 + 6308995*x^12 +...+ A277043(n)*x^n +... which also appears to continue with powers of x^3 only. PROG (PARI) { a(n) = my(m=n + ceil(log(n+3)/log(3)), B=sum(k=0, m, x^(3^k))); polcoeff((B+O(x^(3^m+n+1)))^(n+1)/(n+1), 3^m+n) } for(n=0, 10, print1(a(n), ", ")) CROSSREFS Cf. A144691, A277040, A277042, A277043. Sequence in context: A236044 A285809 A089609 * A087185 A127010 A140547 Adjacent sequences:  A277038 A277039 A277040 * A277042 A277043 A277044 KEYWORD nonn,more AUTHOR Paul D. Hanna, Sep 25 2016 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.

Last modified May 21 17:51 EDT 2022. Contains 353921 sequences. (Running on oeis4.)