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A188289 Binomial sum related to rooted trees. 0
0, 2, 3, 14, 45, 167, 609, 2270, 8517, 32207, 122463, 467843, 1794195, 6903353, 26635773, 103020254, 399300165, 1550554583, 6031074183, 23493410759, 91638191235, 357874310213, 1399137067683, 5475504511859, 21447950506395, 84083979575117 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

FORMULA

a(n) = binomial(2n,n) - (-1)^n - sum( binomial(2k, n-1), k=0..n-1)

a(n) = sum( binomial(n+k,k)*(sum((-1)^r binomial(n-k,r), r=n-k..n), k=1..n)

a(n) = (-1)^n 2^(-(1+n)) (1-2^(1+n)+((-2)^n)*binomial(2+2*n,1+n)*2F1(1,2+2*n;2+n)(-1)

MATHEMATICA

Table[Binomial[2n, n]-(-1)^n-Sum[Binomial[2k, n-1], {k, 0, n-1}], {n, 0, 30}] (* Harvey P. Dale, Dec 10 2012 *)

CROSSREFS

Cf. A000984, A014300, A026641, A178792, A176479, A072547.

Sequence in context: A185895 A128849 A294495 * A153741 A070207 A268559

Adjacent sequences:  A188286 A188287 A188288 * A188290 A188291 A188292

KEYWORD

nonn

AUTHOR

Olivier Gérard, Aug 19 2012

STATUS

approved

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Last modified February 16 12:48 EST 2019. Contains 320163 sequences. (Running on oeis4.)