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A108080
Sum_{i=0..n} C(2n+i,n-i).
4
1, 3, 12, 50, 211, 895, 3805, 16193, 68940, 293526, 1249622, 5318976, 22634700, 96296410, 409573584, 1741574006, 7403616923, 31466106703, 133704121665, 568008916093, 2412570019447, 10245302874071, 43500597657111, 184670002546295, 783850164628721, 3326671128027805, 14116630429874265
OFFSET
0,2
COMMENTS
Apparently a bisection of A026847.
Row sums of A159965. - Paul Barry, Apr 28 2009
LINKS
FORMULA
From Paul Barry, Apr 28 2009: (Start)
G.f.: x/(x*sqrt(1-4x)-(1-2x-(1-3x)*c(x))), c(x) the g.f. of A000108.
a(n) = Sum_{k=0..n} Sum_{j=0..n} C(n+k,j-k)*C(n,j). (End)
From Paul Barry, Sep 07 2009: (Start)
G.f.: (1/sqrt(1-4x))*(1/(1-xc(x)^3)), c(x) the g.f. of A000108.
a(n) = Sum_{k=0..n} C(2n,n-k)*F(k+1) = Sum_{k=0..n} C(2n,k)*F(n-k+1).
a(n) = Sum_{k=0..n} C(2k,k) * A165201(n-k). (End)
Recurrence: n*(17*n-93)*a(n) = 4*(34*n^2 - 189*n + 98)*a(n-1) - 5*(51*n^2 - 271*n + 252)*a(n-2) - 4*(17*n^2 - 184*n + 406)*a(n-3) + 44*(2*n-7) * a(n-4). - Vaclav Kotesovec, Oct 24 2012
a(n) ~ 1/2*(1+1/sqrt(5))*(sqrt(5)+2)^n. - Vaclav Kotesovec, Oct 24 2012
MATHEMATICA
CoefficientList[Series[x/(x*Sqrt[1-4*x]-(1-2*x-(1-3*x)*(1-Sqrt[1-4*x])/(2*x))), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 24 2012 *)
PROG
(PARI) x='x+O('x^66); Vec(x/(x*sqrt(1-4*x)-(1-2*x-(1-3*x)*(1-sqrt(1-4*x))/(2*x)))) \\ Joerg Arndt, May 15 2013
CROSSREFS
Sequence in context: A229665 A092443 A356280 * A113441 A119976 A074547
KEYWORD
nonn
AUTHOR
Ralf Stephan, Jun 03 2005
STATUS
approved