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A101601 G.f.: c(3x)^3, c(x) the g.f. of A000108. 2
1, 9, 81, 756, 7290, 72171, 729729, 7505784, 78298974, 826489170, 8811646074, 94753804536, 1026499549140, 11192793160815, 122744496427425, 1352917116177840, 14979996753469110, 166542316847391870, 1858400773709785470, 20806975169765062200, 233671377667405024620 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..20.

FORMULA

G.f.: 8/(1+sqrt(1-12*x))^3.

a(n) = (3*n+3)/(n+3) * 3^n * C(n+1).

Conjecture: (n+3)*a(n) -3*(5*n+7)*a(n-1) +18*(2*n-1)*a(n-2)=0. - R. J. Mathar, Nov 15 2011

From Amiram Eldar, May 15 2022: (Start)

Sum_{n>=0} 1/a(n) = 51/121 + 964*arcsin(1/(2*sqrt(3)))/(121*sqrt(11)).

Sum_{n>=0} (-1)^n/a(n) = 57/169 + 1204*arcsinh(1/(2*sqrt(3)))/(169*sqrt(13)). (End)

MATHEMATICA

terms = 18;

c[x_] = (1 - Sqrt[1 - 4x])/(2x) + O[x]^terms // Normal;

CoefficientList[c[3x]^3, x][[1 ;; terms]] (* Jean-Fran├žois Alcover, Dec 15 2017 *)

CROSSREFS

Cf. A050159, A101600, A101602.

Sequence in context: A061587 A033145 A158762 * A233737 A344298 A144821

Adjacent sequences:  A101598 A101599 A101600 * A101602 A101603 A101604

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Dec 08 2004

STATUS

approved

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Last modified September 26 08:43 EDT 2022. Contains 356993 sequences. (Running on oeis4.)