The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A210443 G.f.: Sum_{n>=0} x^n * (1 + n^2*x)^n / (1 + x + n^2*x^2)^n. 0
 1, 1, 1, 6, 21, 150, 962, 8640, 80220, 884520, 10709520, 140873040, 2098741680, 32163828480, 568234774800, 9957054159360, 203333391011520, 4013297314266240, 92967912795139200, 2041979786688441600, 52890421861957680000, 1279950952105367942400, 36648398470742114918400 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS a(n) is divisible by ((n-1)/2)! for n>0. Compare to the g.f. of A187741: Sum_{n>=0} x^n*(1+n*x)^n/(1+x+n*x^2)^n = 1/2 + (1+2*x)*Sum_{n>=0} (n+1)!*x^(2*n)/2. LINKS Table of n, a(n) for n=0..22. EXAMPLE G.f.: A(x) = 1 + x + x^2 + 6*x^3 + 21*x^4 + 150*x^5 + 962*x^6 + 8640*x^7 +... where A(x) = 1 + (1+x)*x/(1+x+x^2) + (1+4*x)^2*x^2/(1+x+4*x^2)^2 + (1+9*x)^3*x^3/(1+x+9*x^2)^3 + (1+16*x)^4*x^4/(1+x+16*x^2)^4 + (1+25*x)^5*x^5/(1+x+25*x^2)^5 +... PROG (PARI) {a(n)=polcoeff(sum(m=0, n, x^m*(1+m^2*x)^m/(1+x+m^2*x^2 +x*O(x^n))^m), n)} for(n=0, 30, print1(a(n), ", ")) CROSSREFS Cf. A187741. Sequence in context: A058821 A054366 A304264 * A179768 A131960 A372137 Adjacent sequences: A210440 A210441 A210442 * A210444 A210445 A210446 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 20 2013 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 June 17 05:47 EDT 2024. Contains 373432 sequences. (Running on oeis4.)