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A176479 a(n) = (n+1)*A001003(n). 2
1, 2, 9, 44, 225, 1182, 6321, 34232, 187137, 1030490, 5707449, 31760676, 177435297, 994551222, 5590402785, 31500824304, 177880832001, 1006362234162, 5703029112297, 32367243171740, 183945502869345, 1046646207221582 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Central coefficients T(2n,n) of the Riordan array ((1-x)/(1-2x),x(1-x)/(1-2x)), A105306.

a(n) counts the bi-degree sequences of directed trees (i.e., digraphs whose underlying graph is a tree) with n edges. - Nikos Apostolakis, Dec 31 2016

LINKS

Table of n, a(n) for n=0..21.

V. V. Kruchinin and D. V. Kruchinin, A Method for Obtaining Generating Function for Central Coefficients of Triangles, arXiv preprint arXiv:1206.0877 [math.CO], 2012. - From N. J. A. Sloane, Oct 28 2012

FORMULA

E.g.f.: exp(3x)*Bessel_I(1,2*sqrt(2)x)/sqrt(2) +int(exp(3x)*Bessel_I(1,2*sqrt(2)x)/(sqrt(2)*x),x).

E.g.f.: 1/4 - (x-3)/(4*sqrt(x^2-6*x+1)). - Dmitry Kruchinin, Aug 31 2012

Conjecture: n*(n-1)*a(n) -3*(2*n-1)*(n-1)*a(n-1) +n*(n-2)*a(n-2) = 0. - R. J. Mathar, Dec 03 2014

a(n) = Sum_{k=0..n} binomial(n-1, n-k) * binomial(n+k, n). - Nikos Apostolakis, Dec 31 2016

a(n) = (n+1)*hypergeom([1-n, -n], [2], 2). - Peter Luschny, Jan 02 2017

MATHEMATICA

f[n_] := Sum[Binomial[n - 1, k - 1]*Binomial[n + k, n], {k, 0, n}]; Array[f, 25, 0] (* or *)

CoefficientList[ Series[1/4 - (x - 3)/(4 Sqrt[x^2 - 6x +1]), {x, 0, 25}], x] (* Robert G. Wilson v, Dec 31 2016 *)

Table[(n+1)Hypergeometric2F1[1-n, -n, 2, 2], {n, 0, 21}] (* Peter Luschny, Jan 02 2017 *)

CROSSREFS

Cf. A001003, A105306.

Sequence in context: A013981 A216861 A199308 * A162356 A026302 A214460

Adjacent sequences:  A176476 A176477 A176478 * A176480 A176481 A176482

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 18 2010

STATUS

approved

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Last modified May 29 03:28 EDT 2017. Contains 287242 sequences.