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A138240 Expansion of (1/4)(1-sqrt(1-12x)/sqrt(1-4x)). 2
0, 1, 6, 40, 296, 2400, 20928, 192768, 1848960, 18277888, 184890368, 1904259072, 19898765312, 210424545280, 2247494172672, 24209586782208, 262696649785344, 2868744309571584, 31504024885002240, 347697247933169664 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform of a(n) is -4^comb(n,2)*A099156(n)=-4^comb(n,2)*[x^n](x/(1-8x+4x^2)).

Hankel transform of a(n+1) is 4^comb(n+1,2)=A053763(n+1).

Hankel transform of a(n+2) is 4^comb(n+1,2)*A102591(n+1)=4^comb(n+1,2)*[x^n](6-4x)/(1-8x+4x^2).

LINKS

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

FORMULA

Recurrence: n*a(n) = 4*(4*n-5)*a(n-1) - 48*(n-2)*a(n-2) . - Vaclav Kotesovec, Oct 20 2012

a(n) ~ 2^(2*n-7/2)*3^(n+1/2)/(sqrt(Pi)*n^(3/2)) . - Vaclav Kotesovec, Oct 20 2012

MATHEMATICA

CoefficientList[Series[1/4*(1-Sqrt[1-12*x]/Sqrt[1-4*x]), {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 20 2012 *)

CROSSREFS

Cf. A104498.

Sequence in context: A005037 A081337 A316912 * A083805 A181571 A231126

Adjacent sequences:  A138237 A138238 A138239 * A138241 A138242 A138243

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 07 2008

STATUS

approved

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Last modified January 26 13:09 EST 2022. Contains 350598 sequences. (Running on oeis4.)