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A065140
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a(n) = 2^n*(2*n)!.
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4
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1, 4, 96, 5760, 645120, 116121600, 30656102400, 11158821273600, 5356234211328000, 3278015337332736000, 2491291656372879360000, 2301953490488540528640000, 2541356653499348743618560000
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OFFSET
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0,2
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LINKS
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FORMULA
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Hypergeometric generating function, in Maple notation: 1/sqrt(1-8*x), i.e., a(0)=1, a(n)=round(evalf(subs(x=0, n!*diff(1/(sqrt(1-8*x)), x$n)))), n=1, 2,... Integral representation as n-th moment of a positive function on a positive half-axis: a(n)=int(x^n*exp(-sqrt(x/2))/(2*sqrt(2*x)), x=0..infinity), n=0, 1, ....
G.f.: G(0)/2, where G(k)= 1 + 1/(1 - 4*x*(k+1)*(2*k+1)/(4*x*(k+1)*(2*k+1) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 07 2013
Sum_{n>=0} 1/a(n) = cosh(sqrt(2)/2).
Sum_{n>=0} (-1)^n/a(n) = cos(sqrt(2)/2). (End)
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MATHEMATICA
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PROG
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(PARI) { for (n=0, 100, write("b065140.txt", n, " ", 2^n*(2*n)!) ) } \\ Harry J. Smith, Oct 11 2009
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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