The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A191242 Reversion of x-x^2-x^3-2*x^4 1
 1, 1, 3, 12, 50, 224, 1054, 5121, 25509, 129591, 668811, 3496740, 18481512, 98585788, 530068840, 2869725800, 15630429306, 85589391884, 470905310206, 2601941245750, 14432082902820, 80328808797750, 448527122885700, 2511672193514250 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS For the reversion of x - a*x^2 - b*x^3 - c*x^4 (a!=0, b!=0, c!=0) we have a(n) = sum(k=1,n-1, (sum(j=0..k, a^(-n+3*k-j+1)*b^(n-3*k+2*j-1)*c^(k-j)*binomial(j,n-3*k+2*j-1)*binomial(k,j)))*binomial(n+k-1,n-1))/n, n>1, a(1)=1. LINKS Vincenzo Librandi, Table of n, a(n) for n = 1..200 Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244 [math.CO], 2012. FORMULA a(n) = sum(k=1..n-1, (sum(j=0..k, binomial(j,n-3*k+2*j-1)*2^(k-j)*binomial(k,j)))*binomial(n+k-1,n-1))/n, n>1, a(1)=1. MATHEMATICA a[1] = 1; a[n_] := Sum[Sum[Binomial[j, n - 3k + 2j - 1]*2^(k - j)* Binomial[k, j], {j, 0, k}]*Binomial[n + k - 1, n - 1], {k, 1, n - 1}]/n; Array[a, 24] (* Jean-François Alcover, Jul 23 2018 *) PROG (Maxima) a(n):=sum((sum(binomial(j, n-3*k+2*j-1)*2^(k-j)*binomial(k, j), j, 0, k))*binomial(n+k-1, n-1), k, 1, n-1)/n; (PARI) x='x+O('x^66); /* that many terms */ Vec(serreverse(x-x^2-x^3-2*x^4)) /* show terms */ /* Joerg Arndt, May 28 2011 */ (MAGMA) [&+[Binomial(i, n-3*k+2*i-1)*2^(k-i)*Binomial(k, i)*Binomial(n+k-1, n-1)/n: k in [0..25], i in [0..n]]: n in [1..25]]; // Vincenzo Librandi, Jul 23 2018 CROSSREFS Sequence in context: A074547 A151178 A151179 * A105479 A151180 A268650 Adjacent sequences:  A191239 A191240 A191241 * A191243 A191244 A191245 KEYWORD nonn AUTHOR Vladimir Kruchinin, May 28 2011 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 January 21 04:53 EST 2020. Contains 331104 sequences. (Running on oeis4.)