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A012000
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G.f.: 1/sqrt(1-4*x+16*x^2).
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| 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
| T. D. Noe, Table of n, a(n) for n = 0..200
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FORMULA
| 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
Conjecture: n*a(n) +2*(1-2*n)*a(n-1) +16*(n-1)*a(n-2)=0. - R. J. Mathar, Nov 14 2011
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MATHEMATICA
| Table[ 2^(2n) LegendreP[ n, 1/2 ], {n, 12} ]
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PROG
| (PARI) a(n)=2^(2*n)*subst(pollegendre(n), x, 1/2) (from Michael Somos)
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CROSSREFS
| Sequence in context: A193618 A178955 * A116091 A127262 A121788 A018976
Adjacent sequences: A011997 A011998 A011999 * A012001 A012002 A012003
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KEYWORD
| sign
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AUTHOR
| w.meeussen (wouter.meeussen(AT)pandora.be)
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EXTENSIONS
| G.f. and more terms from Vladeta Jovovic (vladeta(AT)eunet.rs), May 13 2003
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