The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A081698 Expansion of (1 - sqrt( 1 - 4*x*sqrt( 1 + 4*x )) )/( 2*x ). 2
 1, 3, 4, 21, 56, 282, 984, 4813, 19280, 93150, 403672, 1945954, 8845360, 42766292, 200419504, 974134461, 4659558048, 22785183670, 110564976792, 543935554390, 2667398588272, 13196971915628, 65238895435792, 324431740601618, 1614044041864800, 8063536826420460 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 FORMULA G.f.: (1-sqrt(1-4*x*sqrt(1+4*x)))/(2*x). a(n) = sum(k=0..n, (binomial((k+1)/2,n-k)*binomial(2*k,k)*4^(n-k))/(k+1)). [Vladimir Kruchinin, Mar 13 2013] D-finite with recurrence: n*(n+1)*a(n) +2*n*(5*n-7)*a(n-1) +4*(2*n^2-13*n+12)*a(n-2) -8*(2*n-3)*(14*n-37)*a(n-3) +16*(-64*n^2+392*n-573)*a(n-4) -96*(4*n-13)*(4*n-19)*a(n-5)=0. - R. J. Mathar, Jan 23 2020 MAPLE a:= proc(n) option remember; `if`(n<4, [1, 3, 4, 21][n+1],       (2*n*(n+1)*(3-2*n) *a(n-1) +4*n*(2*n-1)*(2*n-3) *a(n-2)        +8*(2*n-3)*(8*n^2-16*n-15) *a(n-3)        +16*(4*n-15)*(4*n-9)*(n+1) *a(n-4)) /(n^2*(n+1)))     end: seq(a(n), n=0..40);  # Alois P. Heinz, Mar 13 2013 MATHEMATICA a[n_] := Sum[Binomial[(k+1)/2, n-k]*Binomial[2*k, k]*4^(n-k)/(k+1), {k, 0, n}]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Apr 02 2015, after Vladimir Kruchinin *) CoefficientList[Series[(1-Sqrt[1-4x Sqrt[1+4x]])/(2x), {x, 0, 30}], x] (* Harvey P. Dale, Oct 30 2017 *) CROSSREFS Cf. A081696. Sequence in context: A034475 A156173 A094632 * A182096 A012123 A012255 Adjacent sequences:  A081695 A081696 A081697 * A081699 A081700 A081701 KEYWORD easy,nonn AUTHOR Emanuele Munarini, Apr 02 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 28 20:44 EDT 2020. Contains 333103 sequences. (Running on oeis4.)