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Search: id:A084769
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| A084769 |
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P_n(9), where P_n is n-th Legendre polynomial; also, a(n) = central coefficient of (1+9*x+20*x^2)^n. |
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+0
1
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| 1, 9, 121, 1809, 28401, 458649, 7544041, 125700129, 2114588641, 35836273449, 610897146201, 10463745263409, 179939616743121, 3104680678772409, 53721299280288201, 931852905510160449, 16198821321758152641
(list; graph; listen)
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OFFSET
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0,2
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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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FORMULA
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G.f.: 1/sqrt(1-18*x+x^2).
Also a(n) = (n+1)-th term of the binomial transform of 1/(1-4x)^(n+1).
E.g.f.: exp(9x)*Bessel_I(0, 2sqrt(20)x); a(n)=sum{k=0..n, C(n, k)C(n+k, k)4^k}; - Paul Barry (pbarry(AT)wit.ie), May 25 2005
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PROGRAM
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(PARI) for(n=0, 30, print1(subst(pollegendre(n), x, 9)", "))
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CROSSREFS
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Sequence in context: A103930 A138978 A046184 this_sequence A050353 A112941 A045976
Adjacent sequences: A084766 A084767 A084768 this_sequence A084770 A084771 A084772
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Jun 03 2003
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