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Search: id:A006442
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| A006442 |
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Expansion of 1/sqrt(1-10x+x^2). |
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+0
1
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| 1, 5, 37, 305, 2641, 23525, 213445, 1961825, 18205345, 170195525, 1600472677, 15122515985, 143457011569, 1365435096485, 13033485491077, 124715953657025, 1195966908404545, 11490534389896325
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Number of Delannoy paths from (0,0) to (n,n) with steps U(0,1), H(1,0) and D(1,1) where H can choose from two colors. - Paul Barry (pbarry(AT)wit.ie), May 25 2005
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REFERENCES
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Tony D. Noe, On the Divisibility of Generalized Central Trinomial Coefficients, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.7.
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..200
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FORMULA
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Legendre polynomial evaluated at 5. - Michael Somos, Dec 04, 2001
G.f.: 1/sqrt(1-10*x+x^2)
Also, a(n) = central coefficient of (1+5*x+6*x^2)^n. - Paul D. Hanna (pauldhanna(AT)juno.com), Jun 03 2003
Also, a(n) equals the (n+1)-th term of the binomial transform of 1/(1-2x)^(n+1). - Paul D. Hanna (pauldhanna(AT)juno.com), Sep 29 2003
a(n)=sum(k=0, n, 2^k*binomial(n, k)*binomial(n+k, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 13 2004
E.g.f.: exp(5x)*Bessel_I(0, 2sqrt(6)x); - Paul Barry (pbarry(AT)wit.ie), May 25 2005
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PROGRAM
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(PARI) a(n)=subst(pollegendre(n), x, 5)
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CROSSREFS
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Sequence in context: A091126 A066381 A078253 this_sequence A084212 A004208 A112698
Adjacent sequences: A006439 A006440 A006441 this_sequence A006443 A006444 A006445
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KEYWORD
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nonn
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AUTHOR
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njas
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