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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
FORMULA
a(n) = Sum_{k=0..n} A039599(n,k)*(-1)^k*5^(n-k). - Philippe Deléham, Dec 11 2007
Integral representation: a(n) = (2/Pi)*Integral_{x=0..20} x^n*sqrt(x*(20-x))/(x*(16+x)). - 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 *)
Table[5^(n + 1) * CatalanNumber[n] * Hypergeometric2F1[1, n + 1/2, n + 2, -5/4]/4, {n, 0, 18}] (* Vaclav Kotesovec, Jun 05 2021 *)
CROSSREFS
Sequence in context: A244559 A319175 A317147 * A294050 A052700 A167540
KEYWORD
nonn
AUTHOR
Philippe Deléham, Nov 18 2007
EXTENSIONS
More terms added by Paul Barry, Sep 15 2009
More terms from Vincenzo Librandi, Feb 11 2014
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)