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!)
 A085362 a(0)=1; for n>0, a(n) = 2*5^(n-1) - (1/2)*Sum_{i=1..n-1} a(i)*a(n-i). 6
 1, 2, 8, 34, 150, 678, 3116, 14494, 68032, 321590, 1528776, 7301142, 35003238, 168359754, 812041860, 3926147730, 19022666310, 92338836390, 448968093320, 2186194166950, 10659569748370, 52037098259090, 254308709196660 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of bilateral Schroeder paths (i.e. lattice paths consisting of steps U=(1,1), D=(1,-1) and H=(2,0)) from (0,0) to (2n,0) and with no H-steps at even (zero, positive or negative) levels. Example: a(2)=8 because we have UDUD, UUDD, UHD, UDDU and their reflections in the x-axis. First differences of A026375. - Emeric Deutsch, Jan 28 2004 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..200 FORMULA G.f.: sqrt((1-x)/(1-5*x)). Sum_{i=0..n} (Sum_{j=0..i} a(j)*a(i-j)) = 5^n. a(n) = (2*(3*n-2)*a(n-1)-5*(n-2)*a(n-2)])n; a(0)=1, a(1)=2. - Emeric Deutsch, Jan 28 2004 a(n) ~ 2*5^(n-1/2)/sqrt(Pi*n). - Vaclav Kotesovec, Oct 14 2012 G.f.: G(0), where G(k)= 1 + 4*x*(4*k+1)/( (4*k+2)*(1-x) - 2*x*(1-x)* (2*k+1)*(4*k+3)/(x*(4*k+3) + (1-x)*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 22 2013 a(n) = Sum_{k=0..n} binomial(2*k,k)*binomial(n-1,n-k). - Vladimir Kruchinin, May 30 2016 a(n) = 2*hypergeom([3/2, 1-n], [2], -4) for n>0. - Peter Luschny, Jan 30 2017 MAPLE a := n -> `if`(n=0, 1, 2*hypergeom([3/2, 1-n], [2], -4)): seq(simplify(a(n)), n=0..22); # Peter Luschny, Jan 30 2017 MATHEMATICA CoefficientList[Series[Sqrt[(1-x)/(1-5x)], {x, 0, 25}], x] PROG (PARI) x='x+O('x^66); Vec(sqrt((1-x)/(1-5*x))) \\ Joerg Arndt, May 10 2013 CROSSREFS Bisection of A026392. Cf. A026375, A026387. Sequence in context: A245090 A151829 A026387 * A150889 A150890 A150891 Adjacent sequences:  A085359 A085360 A085361 * A085363 A085364 A085365 KEYWORD nonn,easy AUTHOR Mario Catalani (mario.catalani(AT)unito.it), Jun 25 2003 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.