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A098557
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Expansion of e.g.f. (1/2)*(1+x)*log((1+x)/(1-x)).
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6
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0, 1, 2, 2, 8, 24, 144, 720, 5760, 40320, 403200, 3628800, 43545600, 479001600, 6706022400, 87178291200, 1394852659200, 20922789888000, 376610217984000, 6402373705728000, 128047474114560000, 2432902008176640000, 53523844179886080000, 1124000727777607680000
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n+1) = n! + (n-1)! * (1-(-1)^n)/2.
conjecture: -a(n) +a(n-1) +(n-1)*(n-3)*a(n-2)=0. - R. J. Mathar, Nov 14 2011
G.f.: 1-G(0), where G(k)= 1 + x*(2*k-1)/(1 - x*(2*k+2)/(x*(2*k+2) + 1/G(k+1))); (continued fraction). - Sergei N. Gladkovskii, Jun 11 2013
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MATHEMATICA
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Join[{0, 1}, Table[(n-1)! + (n-2)!*(1+(-1)^n)/2, {n, 2, 30}]] (* or *) With[{nmax = 50}, CoefficientList[Series[(1/2)*(1 + x)*Log[(1 + x)/(1 - x)], {x, 0, nmax}], x]*Range[0, nmax]!] (* G. C. Greubel, Jan 17 2018 *)
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PROG
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(PARI) for(n=0, 30, print1(if(n==0, 0, if(n==1, 1, (n-1)! + (n-2)!*(1 + (-1)^n)/2)), ", ")) \\ G. C. Greubel, Jan 17 2018
(Magma) [0, 1] cat [Factorial(n-1) + Factorial(n-2)*(1+(-1)^n)/2: n in [2..30]]; // G. C. Greubel, Jan 17 2018
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CROSSREFS
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Cf. A109613 (odd numbers repeated).
Equals the first left hand column of A167552.
Equals the first right hand column of A167556.
(End)
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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