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A157328
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Expansion of 1/(1-2x*c(4x)) with c(x) g.f. of Catalan numbers A000108.
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0
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1, 2, 12, 104, 1072, 12192, 147648, 1867392, 24380160, 326105600, 4445965312, 61555599360, 863154221056, 12233140576256, 174954419109888, 2521749245558784, 36595543723671552, 534249057803698176
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Hankel transform is A122067.
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FORMULA
| a(n)=2^n*A064062(n).
Contribution from Paul Barry (pbarry(AT)wit.ie), 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))*Int(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
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CROSSREFS
| Cf. A000079, A000984, A151374, A110520,
Sequence in context: A052693 A050621 A152254 * A061632 A194951 A104533
Adjacent sequences: A157325 A157326 A157327 * A157329 A157330 A157331
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KEYWORD
| nonn
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AUTHOR
| Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Feb 27 2009
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EXTENSIONS
| Entries corrected by R. J. Mathar, Dec 14 2011
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