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A157328
Expansion of 1/(1-2x*c(4x)) with c(x) g.f. of Catalan numbers (A000108).
0
1, 2, 12, 104, 1072, 12192, 147648, 1867392, 24380160, 326105600, 4445965312, 61555599360, 863154221056, 12233140576256, 174954419109888, 2521749245558784, 36595543723671552, 534249057803698176
OFFSET
0,2
COMMENTS
Hankel transform is A122067.
FORMULA
a(n) = 2^n*A064062(n).
From Paul Barry, Sep 15 2009: (Start)
a(n) = Sum_{k, 0<=k<=n} A039599(n,k)*(-2)^k*4^(n-k).
Integral representation: a(n) = (1/(2*Pi))*Integral(x^n*sqrt(x(16-x))/(x(2+x)),x,0,16). (End)
a(n) = upper left term in M^n, M = an infinite square production matrix as follows:
2, 2, 0, 0, 0, 0, ...
4, 4, 4, 0, 0, 0, ...
4, 4, 4, 4, 0, 0, ...
4, 4, 4, 4, 4, 0, ...
4, 4, 4, 4, 4, 4, ...
...
- Gary W. Adamson, Jul 13 2011
Conjecture: n*a(n) +2*(12-7n)*a(n-1) +16*(3-2n)*a(n-2) = 0. - R. J. Mathar, Dec 14 2011
KEYWORD
nonn
AUTHOR
Philippe Deléham, Feb 27 2009
EXTENSIONS
Entries corrected by R. J. Mathar, Dec 14 2011
STATUS
approved