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%I #19 Jun 03 2019 02:34:16
%S 1,4,25,204,2065,24984,351841,5654440,102131761,2048289660,
%T 45164504281,1085996392404,28281070706785,792955976182384,
%U 23816960356178305,762935687373888144,25963630331068375201,935453627605835395380,35573201479352813399641,1423863512801718371381020
%N Numerator of fraction equal to the continued fraction [0,2,4,...2n].
%F Recurrence equation: a(n+1) = (2*n+2)*a(n) + a(n-1) with a(0) = 1 and a(1) = 1.
%F a(n) = Sum_{k = 0..floor((n-1)/2)} 2^(n-2*k-1)*(n-2*k-1)!*binomial(n-k-1,k)*binomial(n-k,k+1). Cf. A058798. - _Peter Bala_, Aug 01 2013
%F a(n) = 2^(n-1)*n!*hypergeometric([(1-n)/2, 1-n/2],[2, 1-n, -n], 1) for n>=2. - _Peter Luschny_, Sep 14 2014
%t a[n_] := FromContinuedFraction[Range[0, 2n, 2]] // Numerator; Array[a,20] (* _Jean-François Alcover_, Jun 03 2019 *)
%o (Sage)
%o def A036242(n):
%o if n == 1: return 1
%o return 2^(n-1)*factorial(n)*hypergeometric([1/2 - n/2, 1 - n/2], [2, 1-n, -n], 1)
%o [round(A036242(n).n(100)) for n in (1..20)] # _Peter Luschny_, Sep 14 2014
%Y Cf. A036243. A058798.
%K frac,nonn,easy
%O 1,2
%A _Jeff Burch_
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