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Search: id:A071969
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| A071969 |
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Sum( binomial(n+1,k)*binomial(2*n-3*k,n-3*k)/(n+1),k=0..floor(n/3)). |
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5
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| 1, 1, 2, 6, 19, 63, 219, 787, 2897, 10869, 41414, 159822, 623391, 2453727, 9733866, 38877318, 156206233, 630947421, 2560537092, 10435207116, 42689715279, 175243923783, 721649457417, 2980276087005, 12340456995177, 51222441676513, 213090270498764, 888321276659112
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Diagonal of A071946. - Emeric Deutsch (deutsch(AT)duke.poly.edu), Dec 15 2004
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REFERENCES
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D. Merlini et al., Underdiagonal lattice paths with unrestricted steps, Discrete Appl. Math., 91 (1999), 197-213 (d_n page 209).
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LINKS
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D. Merlini et al., Underdiagonal lattice paths with unrestricted steps, Discrete Appl. Math., 91 (1999), 197-213 (d_n page 209).
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FORMULA
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G.f. (offset 1) is series reversion of (x-x^2)/(1+x^3).
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MAPLE
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A071969 := n->add( binomial(n+1, k)*binomial(2*n-3*k, n-3*k)/(n+1), k=0..floor(n/3));
Order:=30: g:=solve(series((H-H^2)/(1+H^3), H)=z, H): seq(coeff(g, z^n), n=1..28); (Deutsch)
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(serreverse((x-x^2)/(1+x^3)+x^2*O(x^n)), n+1))
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CROSSREFS
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Cf. A071946.
Sequence in context: A001170 A001168 A119255 this_sequence A063030 A148467 A148468
Adjacent sequences: A071966 A071967 A071968 this_sequence A071970 A071971 A071972
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Jun 17 2002
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