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A243632 Expansion of ((1-sqrt(1-4*x))/2-sqrt(((-sqrt(1-4*x)-11)*(1-sqrt(1-4*x)))/4+1)+1)/4. 2
0, 1, 2, 7, 30, 144, 744, 4047, 22858, 132830, 789124, 4771086, 29259992, 181569062, 1137891460, 7191411375, 45780189690, 293282202470, 1889328747180, 12231207808050, 79532035376500, 519196901292440 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = (1/n)*Sum_{k=0..n} binomial(n+k-1,k)*binomial(3*n-2,n-4*k-1), n>1, a(0)=0.

A(x) = x*C(x)*S(x*C(x)), where C(x) is g.f. of A000108, S(x) is g.f. of A001003.

a(n) ~ (5*sqrt(2)+7)^(n-1/2) / (sqrt(4*sqrt(2)-5) * sqrt(Pi) * n^(3/2) * 2^(n+5/4)). - Vaclav Kotesovec, Jun 08 2014

O.g.f. A(x) is the series reversion of x*((1 - x)^4 - x^4)/(1 - x)^2. x*A'(x)/A(x) is the o.g.f. for A243644. - Peter Bala, Oct 02 2015

MATHEMATICA

CoefficientList[Series[(3 - Sqrt[1-4*x] - Sqrt[10*Sqrt[1-4*x] - 4*x - 6])/8, {x, 0, 20}], x] (* Vaclav Kotesovec, Jun 08 2014 *)

PROG

(Maxima) a(n):=sum(binomial(n+k-1, k)*binomial(3*n-2, n-4*k-1), k, 0, n)/n;

(PARI) a(n) = if(n==0, 0, sum(k=0, n, binomial(n+k-1, k)*binomial(3*n-2, n-4*k-1)) / n); \\ Altug Alkan, Oct 02 2015

CROSSREFS

Cf. A000108, A001003, A243644.

Sequence in context: A046648 A006013 A187979 * A196148 A193464 A166990

Adjacent sequences:  A243629 A243630 A243631 * A243633 A243634 A243635

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Jun 08 2014

STATUS

approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)