This site is supported by donations to The OEIS Foundation.

 Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS". Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A174123 Partial sums of A002893. 0
 1, 4, 19, 112, 751, 5404, 40573, 313408, 2471167, 19791004, 160459069, 1313922064, 10847561089, 90174127684, 754009158019, 6336733626112, 53489159252671, 453258909448636, 3854034482891725, 32871004555812112, 281127047928811201 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Partial sums of (2n)-th moment of the distance from the origin of a 3-step random walk in the plane. The subsequence of primes in this partial sum begins: 19, 751, 10847561089, 53489159252671. LINKS Tewodros Amdeberhan and Roberto Tauraso, Two triple binomial sum supercongruences, arXiv:1607.02483 [math.NT], Jul 08 2016. FORMULA a(n) = SUM[i=0..n] A002893(i) = SUM[i=0..n] SUM[p+q+r=i} (i!/(p!q!r!))^2 with p,q,r >=0. From Sergey Perepechko Feb 16 2011: (Start) O.g.f.: 2*sqrt(2)/Pi/(1-z)/sqrt(1-6*z-3*z^2+sqrt((1-z)^3*(1-9*z)))* EllipticK(8*z^(3/2)/(1-6*z-3*z^2+sqrt((1-z)^3*(1-9*z)))). 9*(n+2)^2*a(n) - (99+86*n+19*n^2)*a(n+1) + (72+56*n+11*n^2)*a(n+2) - (n+3)^2*a(n+3)=0. (End) a(n) ~ 3^(2*n + 7/2) / (32*Pi*n). - Vaclav Kotesovec, Jul 11 2016 MATHEMATICA Accumulate[Table[Sum[Binomial[n, k]^2 Binomial[2k, k], {k, 0, n}], {n, 0, 20}]] (* Harvey P. Dale, May 05 2013 *) PROG (PARI) a(n)=sum(m=0, n, sum(k=0, m, binomial(m, k)^2*binomial(2*k, k))) CROSSREFS Cf. A002893, A000172, A002895, A000984. Sequence in context: A004212 A243241 A060905 * A127548 A122835 A013185 Adjacent sequences:  A174120 A174121 A174122 * A174124 A174125 A174126 KEYWORD easy,nonn AUTHOR Jonathan Vos Post, Mar 08 2010 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 | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.