This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A174783 Expansion of (1+2x-sqrt(1-4x^2))/(2(1-x^2)*sqrt(1-4x^2)). 4
 0, 1, 1, 3, 4, 9, 14, 29, 49, 99, 175, 351, 637, 1275, 2353, 4707, 8788, 17577, 33098, 66197, 125476, 250953, 478192, 956385, 1830270, 3660541, 7030570, 14061141, 27088870, 54177741, 104647630 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Hankel transform is A174784. Hankel transform of a(n+1) is A174785. Transform of the sequence 0,1,1,1,1,0,0,1,1,1,1,0,0,1,.. by the Riordan array (c(x^2),xc(x^2)), c(x) the g.f. of A000108. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 FORMULA E.g.f.: int(cosh(x-t)*(Bessel_I(0,2t)+Bessel_I(1,2t)),t,0,x). Conjecture: n*a(n) -2*a(n-1) +(8-5*n)*a(n-2) +2*a(n-3) +4*(n-2)*a(n-4)=0. - R. J. Mathar, Nov 13 2012 a(n) ~ 2^(n+3/2)/(3*sqrt(Pi*n)). - Vaclav Kotesovec, Feb 04 2014 a(n) = Sum_{i=1..(n+1)/2}((binomial(n-2*i+1,floor((n-2*i+1)/2)))). - Vladimir Kruchinin, Mar 15 2016 MATHEMATICA CoefficientList[Series[(1 + 2 x - Sqrt[1 - 4 x^2])/(2 (1 - x^2) Sqrt[1 - 4 x^2]), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 04 2014 *) PROG (Maxima) a(n):=sum((binomial(n-2*i+1, floor((n-2*i+1)/2))), i, 1, (n+1)/2); /* - Vladimir Kruchinin, Mar 15 2016 */ CROSSREFS Sequence in context: A051841 A096081 A054162 * A183203 A321680 A215667 Adjacent sequences:  A174780 A174781 A174782 * A174784 A174785 A174786 KEYWORD easy,nonn AUTHOR Paul Barry, Mar 29 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 15 04:33 EDT 2019. Contains 328026 sequences. (Running on oeis4.)