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A026855 a(n) = T(2n+1,n+2), T given by A026736. 1
1, 5, 21, 85, 342, 1380, 5598, 22836, 93640, 385734, 1595232, 6619374, 27545269, 114901685, 480282369, 2011058681, 8433331523, 35410037683, 148842787215, 626234799703, 2636930617597, 11111302351505, 46848507630321, 197631791675365 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Robert Israel, Table of n, a(n) for n = 1..1580

FORMULA

G.f.: (x*C(x)^4)/(1 - x/sqrt(1 - 4*x)) where C(x) is the g.f. for Catalan numbers A000108. - David Callan, Jan 16 2016

a(n) ~ (3 - sqrt(5))^4 * (2 + sqrt(5))^(n+2) / (16*sqrt(5)). - Vaclav Kotesovec, Jul 18 2019

MAPLE

gf := ((-2*x^3+12*x^2-7*x+1)*sqrt(1-4*x)+16*x^3-24*x^2+9*x-1)/(2*(x^2+4*x-1)*x^3):

S:= series(gf, x, 40):

seq(coeff(S, x, j), j=1..30); # Robert Israel, Jan 17 2016

MATHEMATICA

CoefficientList[Series[(1-Sqrt[1-4x])^4/(16*x^4*(1-x/Sqrt[1-4x])), {x, 0, 30}], x] (* David Callan, Jan 16 2016 *)

PROG

(PARI) my(x='x+O('x^30)); Vec( sqrt(1-4*x)*(1-sqrt(1-4*x))^4/(16*x^3*(sqrt(1-4*x) -x)) ) \\ G. C. Greubel, Jul 17 2019

(MAGMA) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!( Sqrt(1-4*x)*(1-Sqrt(1-4*x))^4/(16*x^3*(Sqrt(1-4*x) -x)) )); // G. C. Greubel, Jul 17 2019

(Sage) a=(sqrt(1-4*x)*(1-sqrt(1-4*x))^4/(16*x^3*(sqrt(1-4*x) -x))).series(x, 30).coefficients(x, sparse=False); a[1:] # G. C. Greubel, Jul 17 2019

CROSSREFS

Cf. A000108, A026736.

Sequence in context: A084241 A002450 A187063 * A272832 A273489 A097113

Adjacent sequences:  A026852 A026853 A026854 * A026856 A026857 A026858

KEYWORD

nonn

AUTHOR

Clark Kimberling

STATUS

approved

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Last modified December 4 10:59 EST 2021. Contains 349486 sequences. (Running on oeis4.)