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A006320
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Royal paths in a lattice.
(Formerly M4200)
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4
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1, 6, 30, 146, 714, 3534, 17718, 89898, 461010, 2386390, 12455118, 65478978, 346448538, 1843520670, 9859734630, 52974158938, 285791932578, 1547585781414, 8408765223294
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| G. Kreweras, Sur les hi\'{e}rarchies de segments, Cahiers Bureau Universitaire Recherche Op\'{e}rationnelle, Cahier 20, Inst. Statistiques, Univ. Paris, 1973.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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FORMULA
| 3-fold convolution of the large Schroeder numbers (A006318). G.f.=R^3, where R=[1-z-sqrt(1-6z+z^2)]/(2z) is the g.f. of A006318. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 15 2004
a(n)=(3/n)*sum(binomial(n, j)*binomial(n+2+j, n-1), j=0..n) (n>0). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Aug 19 2004
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MAPLE
| 1, seq(3*sum(binomial(n, j)*binomial(n+2+j, n-1), j=0..n)/n, n=1..18);
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CROSSREFS
| Third diagonal of A033877
Cf. A006318.
Sequence in context: A135160 A046945 A089817 * A079738 A127741 A073965
Adjacent sequences: A006317 A006318 A006319 * A006321 A006322 A006323
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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