A200966 Expansion (1-sqrt(1-4*x))/(2*(1-x^4-x)).

1, 2, 4, 9, 24, 68, 204, 642, 2096, 7026, 24026, 83454, 293562, 1043488, 3741954, 13520253, 49171485, 179859763, 661240417, 2442023860, 9055315765, 33701442548, 125845246605, 471346884115, 1770306347204, 6665954191204, 25159152509961

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

a(n) = Sum_{i=0..(n-1)} (Sum_{j=0..(i/3)} binomial(i-3*j,j))*binomial(2*(n-i)-2,n-i-1))/(n-i)), n>0.

D-finite with recurrence: n*a(n) +n*a(n-1) +2*(30-13n)*a(n-2) +12*(2n-5)*a(n-3) -n*a(n-4) -2n*a(n-5) +12*(2n-5)*a(n-6)=0. - R. J. Mathar, Nov 26 2011

a(n) ~ 2^(2*n+6) / (191*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Jan 31 2014

Mathematica

Rest[CoefficientList[Series[(1-Sqrt[1-4x])/(2(1-x^4-x)), {x, 0, 40}], x]] (* Harvey P. Dale, May 08 2013 *)

Prog

(Maxima)
a(n):=sum(((sum(binomial(i-3*j, j), j, 0, i/3))*binomial(2*(n-i)-2, n-i-1))/(n-i), i, 0, n-1);
(PARI) x='x+O('x^50); Vec((1-sqrt(1-4*x))/(2*(1-x^4-x))) \\ G. C. Greubel, May 27 2017

Crossrefs

Sequence in context: A148081 A148082 A148083 * A148084 A156804 A081913

Adjacent sequences: A200963 A200964 A200965 * A200967 A200968 A200969

Keyword

nonn

Author

Vladimir Kruchinin, Nov 25 2011

Status

approved