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!)
 A226312 Sum_{k=0..n} k*binomial(n,k)^2*binomial(2*k,k). 1
 0, 2, 20, 186, 1704, 15510, 140676, 1273230, 11508048, 103919022, 937787100, 8458728630, 76269112200, 687496910490, 6195793616460, 55827244680930, 502959206683296, 4530723835554270, 40809306881317068, 367548287590324902, 3310080578306654520 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 Bruno Haible, Combinatorial proof of a binomial identity, 1992. FORMULA a(n) ~ 3^(2*n+1/2)/(2*Pi). - Vaclav Kotesovec, Jun 10 2013 Recurrence: (n-2)*n*(n-1)*a(n) = (n-2)*(10*n^2-10*n+3)*a(n-1) - 9*(n-1)^3*a(n-2). - Vaclav Kotesovec, Jun 10 2013 G.f.: 2*x*((5+3*x)*(1-9*x)^2*hypergeom([2/3, 2/3],[1],-27*x*(1-x)^2/(1-9*x)^2)-4*(1-x)*(1+3*x)^3*hypergeom([5/3, 5/3],[2],-27*x*(1-x)^2/(1-9*x)^2))/(1-9*x)^(13/3).  - Mark van Hoeij, Apr 11 2014 MAPLE f:=n->add(k*binomial(n, k)^2*binomial(2*k, k), k=0..n); [seq(f(n), n=0..40)]; MATHEMATICA Table[Sum[k*Binomial[n, k]^2*Binomial[2*k, k], {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jun 10 2013 *) CROSSREFS Sequence in context: A279462 A037566 A125857 * A171076 A287999 A001078 Adjacent sequences:  A226309 A226310 A226311 * A226313 A226314 A226315 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 08 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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 6 07:05 EST 2019. Contains 329784 sequences. (Running on oeis4.)