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%I #15 Aug 01 2018 10:24:30
%S 0,2,20,150,1256,12650,151932,2127230,34035920,612646866,12252937700,
%T 269564629862,6469551117240,168208329048890,4709833213369676,
%U 141294996401091150,4521439884834917792,153728956084387206050
%N a(n) = (a(n-1)+(2n-1))*(2n) with a(0) = 0.
%H Altug Alkan, <a href="/A093302/b093302.txt">Table of n, a(n) for n = 0..1000</a>
%F a(n) = 2 * floor(e^(1/2) * n! * 2^n) - 2n - 2.
%F E.g.f.: (2x+4x^2)/(1-2x) * exp(x).
%F a(n) = 2*A271476(n) for n >= 1. - _Altug Alkan_, Aug 01 2018
%t RecurrenceTable[{a[0]==0,a[n]==(a[n-1]+2n-1)2n},a,{n,20}] (* _Harvey P. Dale_, May 20 2014 *)
%o (PARI) a(n)=2*floor(exp(1/2)*n!*2^n)-2*n-2
%o (PARI) x='x+O('x^99); concat(0, Vec(serlaplace((2*x+4*x^2)/(1-2*x)*exp(x)))) \\ _Altug Alkan_, Aug 01 2018
%o (PARI) a=vector(99); a[1]=2; for(n=2, #a, a[n] = 2*(a[n-1]+2*n-1)*n); concat(0,a) \\ _Altug Alkan_, Aug 01 2018
%Y a(n) = A007566(n)-1 = 2*A010844(n)-2n-2. Bisection of A077138.
%Y Cf. A271476.
%K easy,nonn
%O 0,2
%A Emrehan Halici (emrehan(AT)halici.com.tr), Apr 24 2004
%E Edited by _Ralf Stephan_, Apr 26 2004
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