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A116421
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2^(n-1)*binomial(2n-1,n-1)^2.
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1
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0, 1, 18, 400, 9800, 254016, 6830208, 188457984, 5300380800, 151289881600, 4369251780608, 127394382495744, 3743979352236032, 110768619888640000, 3295931587706880000, 98555678764852838400, 2959750227906986803200
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..100
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FORMULA
| G.f.: 1+(K(32x)-1)/4 where K(k)=Elliptic_F(pi/2,k) is the complete Elliptic integral of the first kind; E.g.f.: BesselI(0, 2*sqrt(2)x)*BesselI(1, 2*sqrt(2)x)/sqrt(2); a(n)=2^(n+1)*(binomial(2n,n)/4)^2-0^n/8.
Conjecture: n^2*a(n) -(2*n-1)^2*a(n-1)=0. - R. J. Mathar, Nov 16 2011
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PROG
| (MAGMA) [2^(n-1)*Binomial(2*n-1, n-1)^2: n in [0..20]]; // Vincenzo Librandi, Nov 17 2011
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CROSSREFS
| Cf. A060150.
Sequence in context: A070943 A159647 A111454 * A172135 A005477 A197343
Adjacent sequences: A116418 A116419 A116420 * A116422 A116423 A116424
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 14 2006
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