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A115902
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Expansion of (1-8*x)^(-3/2).
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0
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1, 12, 120, 1120, 10080, 88704, 768768, 6589440, 56010240, 472975360, 3972993024, 33228668928, 276905574400, 2300446310400, 19060840857600, 157569617756160, 1299949346488320, 10705465206374400, 88022713919078400
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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FORMULA
| G.f.: 1/((1-8*x)*sqrt(1-8*x)).
a(n) = Jacobi_P(n,1/2,1/2,1)*8^n.
a(n) = 2^n*(2*n+1)*binomial(2*n,n)
a(n) = (2*n+1)*A059304(n).
a(n) = 2^n*A002457(n).
Conjecture: n*a(n) -4*(2*n+1)*a(n-1) =0. - R. J. Mathar, Nov 14 2011
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MAPLE
| a:=n->sum((binomial(2*n, n))*2^(n-2), j=1..n): seq(a(n), n=1..19); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 03 2007
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CROSSREFS
| Sequence in context: A009140 A012273 A008465 * A004332 A129329 A129332
Adjacent sequences: A115899 A115900 A115901 * A115903 A115904 A115905
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 02 2006
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