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Search: id:A012000
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| A012000 |
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G.f.: 1/sqrt(1-4*x+16*x^2). |
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+0
4
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| 1, 2, -2, -28, -74, 92, 1324, 3656, -4826, -70228, -197372, 267896, 3921724, 11126936, -15347432, -225505648, -643622906, 897078476, 13214495764, 37869162392, -53170602284, -784672445368, -2255295815192, 3183829452272, 47051201187676, 135537088268792, -192142210448216
(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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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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Scaled Legendre polynomials evaluated at 1/2: 2^(2n)P(n, 1/2). - Michael Somos, Dec 03, 2001
a(n)=(-1)^n*sum(k=0, n, binomial(n, k)^2*(-3)^k). - Benoit Cloitre, Oct 25 2003
a(n)=sum{k=0..floor(n/2), binomial(n, k)binomial(2(n-k), n)(-4)^k} - Paul Barry (pbarry(AT)wit.ie), Sep 08 2004
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MATHEMATICA
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Table[ 2^(2n) LegendreP[ n, 1/2 ], {n, 12} ]
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PROGRAM
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(PARI) a(n)=2^(2*n)*subst(pollegendre(n), x, 1/2) (from Michael Somos)
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CROSSREFS
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Sequence in context: A024577 A121222 A125067 this_sequence A116091 A127262 A121788
Adjacent sequences: A011997 A011998 A011999 this_sequence A012001 A012002 A012003
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KEYWORD
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sign
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AUTHOR
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w.meeussen (wouter.meeussen(AT)pandora.be)
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EXTENSIONS
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G.f. and more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), May 13 2003
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