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Search: id:A084768
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| A084768 |
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P_n(7), where P_n is n-th Legendre polynomial; also, a(n) = central coefficient of (1+7*x+12*x^2)^n. |
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+0
1
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| 1, 7, 73, 847, 10321, 129367, 1651609, 21360031, 278905249, 3668760487, 48543499753, 645382441711, 8614382884849, 115367108888311, 1549456900170553, 20861640747345727, 281483386791966529
(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(1-14*x+x^2).
Also a(n) = (n+1)-th term of the binomial transform of 1/(1-3x)^(n+1).
a(n)=sum(k=0, n, 3^k*binomial(n, k)*binomial(n+k, k)) - Benoit Cloitre (benoit7848c(AT)orange.fr), Apr 13 2004
E.g.f.: exp(7x)*Bessel_I(0, 2sqrt(12)x); - 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, 7)", "))
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CROSSREFS
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Adjacent sequences: A084765 A084766 A084767 this_sequence A084769 A084770 A084771
Sequence in context: A121127 A071060 A099141 this_sequence A106651 A114429 A124547
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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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