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A174227 Expansion of (1-10x+sqrt((1-10x)(1-14x))/(2x). 1
1, 1, 12, 145, 1764, 21602, 266232, 3301349, 41178660, 516512462, 6513158376, 82542517386, 1051024082472, 13442267711940, 172638285341040, 2225824753934445, 28802104070304420, 373966734921011990 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform is A077417. The g.f. A(x) satisfies the continued fraction relation

A(x)=1/(1-x/(1-10x-x*A(x)).

LINKS

Table of n, a(n) for n=0..17.

FORMULA

a(n) = sqrt(5/7) * 10^n * (6*hypergeom([1/2, n+1],[1],2/7)-7*hypergeom([1/2, n],[1],2/7)) / (n+1) for n > 0. [From Mark van Hoeij, Jul 02 2010]

Conjecture: (n+1)*a(n) +12*(1-2*n)*a(n-1) +140*(n-2)*a(n-2)=0. - R. J. Mathar, Sep 30 2012

CROSSREFS

Sequence in context: A055332 A288792 A041061 * A041266 A015501 A039493

Adjacent sequences:  A174224 A174225 A174226 * A174228 A174229 A174230

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 12 2010

STATUS

approved

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Last modified January 29 02:10 EST 2022. Contains 350672 sequences. (Running on oeis4.)