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A217275 Expansion of 2/(1-x+sqrt(1-2*x-27*x^2)). 7
1, 1, 8, 22, 141, 561, 3291, 15583, 88691, 459187, 2599570, 14136200, 80391235, 450046143, 2579291352, 14710321998, 85002979083, 491050703739, 2859262171872, 16674374605722, 97747766045679, 574231140306699, 3385974360904227, 20009363692187115, 118582649963026677 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

Generally for G.f. = 2/(1-x+sqrt(1-2x-(4*z-1)*x^2)) is asymptotic

a(n) ~ (1+2*sqrt(z))^(n+3/2)/(2*sqrt(Pi)*z^(3/4)*n^(3/2)); here we have the case z=7.

General recurrence: (n+2)*a(n)=(2*n+1)*a(n-1)+(4*z-1)*(n-1)*a(n-2);; here with z=7.

G.f.: 1/(1 - x - 7*x^2/(1 - x - 7*x^2/(1 - x - 7*x^2/(1 - x - 7*x^2/(1 - ....))))), a continued fraction. - Ilya Gutkovskiy, May 26 2017

MATHEMATICA

Table[SeriesCoefficient[2/(1-x+Sqrt[1-2*x-27*x^2]), {x, 0, n}], {n, 0, 25}]

Table[Sum[Binomial[n, 2k]*Binomial[2k, k]*7^k/(k+1), {k, 0, n}], {n, 0, 25}]

CROSSREFS

Cf. A001006 (z=1), A025235 (z=2), A025237 (z=3), A091147 (z=4), A091148 (z=5), A091149 (z=6).

Sequence in context: A264631 A026593 A131622 * A183308 A117613 A215740

Adjacent sequences:  A217272 A217273 A217274 * A217276 A217277 A217278

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Sep 29 2012

STATUS

approved

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Last modified January 17 18:28 EST 2018. Contains 297829 sequences.