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

 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!)
 A217042 G.f.: 1 = Sum_{n>=0} a(n) * x^n * Sum_{k=0..2*n+1} binomial(2*n+1,k)^2 * (-x)^k. 0
 1, 1, 9, 216, 9685, 690129, 71218224, 10016312400, 1839013713405, 426795483514725, 122096137679279577, 42196285096882327872, 17327812666870134181584, 8338575020551966129589776, 4647348123388957546230426120, 2969504710005383652330487580832 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Compare g.f. to: 1 = Sum_{n>=0} A001764(n)*x^n * Sum_{k=0..2*n+1} C(2*n+1,k)*(-x)^k where A001764(n) = C(3*n+1,n)/(3*n+1). LINKS EXAMPLE G.f.: A(x) = 1 + x + 9*x^2 + 216*x^3 + 9685*x^4 + 690129*x^5 +... The coefficients satisfy: 1 = 1*(1 - x) + 1*x*(1 - 3^2*x^1 + 3^2*x^2 - x^3) + 9*x^2*(1 - 5^2*x^1 + 10^2*x^2 - 10^2*x^3 + 5^2*x^4 - x^5) + 216*x^3*(1 - 7^2*x^1 + 21^2*x^2 - 35^2*x^3 + 35^2*x^4 - 21^2*x^5 + 7^2*x^6 - x^7) + 9685*x^4*(1 - 9^2*x^1 + 36^2*x^2 - 84^2*x^3 + 126^2*x^4 - 126^2*x^5 + 84^2*x^6 - 36^2*x^7 + 9^2*x^8 - x^9) + 690129*x^5*(1 - 11^2*x^1 + 55^2*x^2 - 165^2*x^3 + 330^2*x^4 - 462^2*x^5 + 462^2*x^6 - 330^2*x^7 + 165^2*x^8 - 55^2*x^9 + 11^2*x^10 - x^11) +... PROG (PARI) {a(n)=if(n==0, 1, -polcoeff(sum(m=0, n-1, a(m)*x^m*sum(k=0, 2*m+1, binomial(2*m+1, k)^2*(-x)^k)+x*O(x^n)), n))} for(n=0, 31, print1(a(n), ", ")) CROSSREFS Cf. A180716, A001764. Sequence in context: A250548 A007108 A007107 * A064633 A084942 A061718 Adjacent sequences: A217039 A217040 A217041 * A217043 A217044 A217045 KEYWORD nonn AUTHOR Paul D. Hanna, Sep 25 2012 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 December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)