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A174107 Expansion of (1/(1-x+x^2))c(x/(1-x+x^2)), c(x) the g.f. of A000108. 3
1, 2, 4, 11, 37, 134, 505, 1964, 7834, 31880, 131833, 552392, 2340181, 10007048, 43136554, 187244489, 817754563, 3590696546, 15842313289, 70198094315, 312258202582, 1393879987262, 6241982874715, 28034051706962 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Binomial transform of A061639(n+1).
Hankel transform is A174108.
LINKS
FORMULA
Conjecture: (n+1)*a(n) +2*(1-3n)*a(n-1) +7*(n-1)*a(n-2) +2*(5-3*n)*a(n-3) +(n-3)*a(n-4)=0. - R. J. Mathar, Nov 15 2011
G.f.: (1 - 1/G(0))/(2*x), where G(k)= 1 + 4*x*(4*k+1)/( (1-x+x^2)*(4*k+2) - x*(1-x+x^2)*(4*k+2)*(4*k+3)/(x*(4*k+3) + (1-x+x^2)*(k+1)/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 27 2013
G.f.: (1 - sqrt( (1 - 5*x + x^2) / (1 - x + x^2)))/(2*x). - Sergei N. Gladkovskii, Jun 27 2013
a(n) ~ sqrt(105+23*sqrt(21)) * (5+sqrt(21))^n / (sqrt(Pi) * n^(3/2) * 2^(n+7/2)). - Vaclav Kotesovec, Feb 04 2014
MATHEMATICA
CoefficientList[Series[(1 - Sqrt[(1 - 5 x + x^2)/(1 - x + x^2)])/(2 x), {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 04 2014 *)
CROSSREFS
Sequence in context: A086611 A035098 A328425 * A253927 A281481 A138301
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 07 2010
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)