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A018224
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C(n,[ n/2 ])^2.
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3
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1, 1, 4, 9, 36, 100, 400, 1225, 4900, 15876, 63504, 213444, 853776, 2944656, 11778624, 41409225, 165636900, 590976100, 2363904400, 8533694884, 34134779536, 124408576656, 497634306624, 1828114918084
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| a(n) is also the number of rooted two-vertex (or, dually, two-face) regular planar maps of valency n+1. - Valery A. Liskovets (liskov(AT)im.bas-net.by), Oct 19 2005
If A is a random matrix in USp(4) (4 X 4 complex matrices that are unitary and symplectic), then a(n)=(-1)^n*E[(tr(A^4))^n]. - Andrew V. Sutherland (drew(AT)math.mit.edu), Apr 01 2008
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REFERENCES
| M. Bousquet, G. Labelle and P. Leroux, Enumeration of planar two-face maps, Discrete Math., vol. 222 (2000), 1-25.
Kiran S. Kedlaya and Andrew V. Sutherland, "Hyperelliptic curves, L-polynomials and random matrices", preprint, 2008.
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LINKS
| Kiran S. Kedlaya and Andrew V. Sutherland, Hyperelliptic curves, L-polynomials and random matrices.
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FORMULA
| E.g.f.: BesselI(0, 2*x)*(BesselI(0, 2*x)+BesselI(1, 2*x)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 12 2005
G.f. (1+1/(4x))*hypergeom([1/2, 1/2],[1],16*x^2)-1/(4x) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Oct 13 2009]
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CROSSREFS
| A001405(n)^2.
Bisections are A002894 and A060150.
Cf. A113182.
Cf. A138545.
Sequence in context: A133125 A126161 A179934 * A149137 A149138 A149139
Adjacent sequences: A018221 A018222 A018223 * A018225 A018226 A018227
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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