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A174227 Expansion of -(10*x + sqrt((1-10*x)*(1-14*x)))/(2*x). 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/(1-10*x-x*A(x))).
LINKS
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. - Mark van Hoeij, Jul 02 2010
D-finite with recurrence: (n+1)*a(n) +12*(1-2*n)*a(n-1) +140*(n-2)*a(n-2)=0. - R. J. Mathar, Sep 30 2012
MAPLE
with(LREtools): with(FormalPowerSeries): # requires Maple 2022
ogf:= -(10*x + sqrt((1-10*x)*(1-14*x)))/(2*x): req:= FindRE(ogf, x, u(n));
init:= [1, 1, 12, 145]: iseq:= seq(u(i-1)=init[i], i=1..nops(init)):
rmin:= subs(n=n-2, MinimalRecurrence(req, u(n), {iseq})[1]); # Mathar's recurrence
a:= gfun:-rectoproc({rmin, iseq}, u(n), remember):
seq(a(n), n=0..17); # Georg Fischer, Nov 03 2022
# Alternative, using function FindSeq from A174403:
ogf := -(10*x + sqrt((1-10*x)*(1-14*x)))/(2*x):
a := FindSeq(ogf): seq(a(n), n=0..17); # Peter Luschny, Nov 04 2022
CROSSREFS
Sequence in context: A055332 A288792 A041061 * A041266 A015501 A039493
KEYWORD
nonn,easy
AUTHOR
Paul Barry, Mar 12 2010
EXTENSIONS
Definiton corrected by Peter Luschny, Nov 05 2022
STATUS
approved

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Last modified July 20 14:37 EDT 2024. Contains 374446 sequences. (Running on oeis4.)