A132864 Expansion of 1/(1-4x*c(5x)), where c(x) is the g.f. of A000108.
1, 4, 36, 424, 5716, 83544, 1288296, 20637264, 340116276, 5730014584, 98241641656, 1708602483504, 30070563388936, 534554579527024, 9584333758817616, 173120386421418144, 3147337611202622196, 57545643875054919864, 1057492201661230657176
Offset: 0
Keywords
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
Programs
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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 *)
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
Extensions
More terms added by Paul Barry, Sep 15 2009
More terms from Vincenzo Librandi, Feb 11 2014
Comments