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A132864 Expansion of 1/(1-4x*c(5x)), where c(x) is the g.f. of A000108 . 3
1, 4, 36, 424, 5716, 83544, 1288296, 20637264, 340116276, 5730014584, 98241641656, 1708602483504, 30070563388936, 534554579527024, 9584333758817616, 173120386421418144, 3147337611202622196, 57545643875054919864, 1057492201661230657176 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is A135420. [Paul Barry, Sep 15 2009]

LINKS

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

FORMULA

a(n) = Sum_{k, 0<=k<=n}A039599(n,k)*(-1)^k*5^(n-k). - Philippe Deléham, Dec 11 2007

Integral representation: a(n)=(2/pi)*Int(x^n*sqrt(x(20-x))/(x(16+x)),x,0,20). [Paul Barry, Sep 15 2009]

From Gary W. Adamson, Jul 18 2011: (Start)

a(n) = upper left term in M^n, M = an infinite square production matrix as follows:

4, 4, 0, 0, 0, 0,...

5, 5, 5, 0, 0, 0,...

5, 5, 5, 5, 0, 0,...

5, 5, 5, 5, 5, 0,...

5, 5, 5, 5, 5, 5,...

... (end)

Conjecture: n*a(n)+2*(15-2*n)*a(n-1) +160*(3-2*n)*a(n-2)=0. - R. J. Mathar, Nov 15 2011

a(n) ~ 4^n * 5^(n+1) / (9 * n^(3/2) * sqrt(Pi)). - Vaclav Kotesovec, Feb 08 2014

MATHEMATICA

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

CROSSREFS

Sequence in context: A202828 A131765 A244559 * A294050 A052700 A167540

Adjacent sequences:  A132861 A132862 A132863 * A132865 A132866 A132867

KEYWORD

nonn

AUTHOR

Philippe Deléham, Nov 18 2007

EXTENSIONS

More terms added. Paul Barry, Sep 15 2009

More terms from Vincenzo Librandi, Feb 11 2014

STATUS

approved

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Last modified February 22 21:22 EST 2018. Contains 299469 sequences. (Running on oeis4.)