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A110166 Row sums of Riordan array A110165. 3
1, 4, 18, 85, 410, 1999, 9807, 48304, 238570, 1180615, 5851253, 29033074, 144190943, 716652070, 3564079250, 17734184365, 88280673770, 439625873215, 2189988826125, 10912480440850, 54389237971285, 271142650382080 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of 5-ary words of length n in which the number of 1's does not exceed the number of 0's. - David Scambler, Aug 14 2012

LINKS

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

FORMULA

G.f.: (1/sqrt(1-6*x+5*x^2))/(1-(1-3*x-sqrt(1-6*x+5*x^2))/(2*x)).

a(n) = sum{k=0..n, sum{j=0..n, C(n, j)*C(2*j, j+k)}}.

Recurrence: n*a(n) = (11*n-8)*a(n-1) - 5*(7*n-10)*a(n-2) + 25*(n-2)*a(n-3). - Vaclav Kotesovec, Oct 18 2012

a(n) ~ 5^n/2*(1+sqrt(5)/(2*sqrt(Pi*n))). - Vaclav Kotesovec, Oct 18 2012

MATHEMATICA

Table[Sum[Sum[Binomial[n, j]Binomial[2j, j+k], {j, 0, n}], {k, 0, n}], {n, 0, 25}] (* Harvey P. Dale, Dec 16 2011 *)

CROSSREFS

Sequence in context: A007859 A185132 A085923 * A046885 A247637 A055834

Adjacent sequences:  A110163 A110164 A110165 * A110167 A110168 A110169

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 14 2005

STATUS

approved

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Last modified October 16 12:35 EDT 2018. Contains 316263 sequences. (Running on oeis4.)