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%I #14 Jan 09 2021 15:41:14
%S 1,0,14,870,18796230,28634752793916486,
%T 187118328452563149209991044344449606,
%U 22533823529098462258163079522899558179092788838542277982316450977506091590
%N a(n) = A340312(n, 2^(n-1)). a(n) is the central term of row n of A340312.
%C a(9) = 2299131884087642202247291403507120751687796592498104258 * C, where C is a composite factor with 96 digits.
%C C = P47*P49, with P47 = 88967307877356450624418823383132738084943851019 and
%C P49 = 4512180962860489443011495305279720577473472225641. - _Hugo Pfoertner_, Jan 09 2021
%H Andrew Howroyd, <a href="/A340259/b340259.txt">Table of n, a(n) for n = 1..11</a>
%F a(n) = (2*binomial(2^n-1, 2^(n-1)) + (2^n-1)*binomial(2^(n-1), 2^(n-2)))/2^n for n >= 3. - _Andrew Howroyd_, Jan 09 2021
%p seq(A340312_row(n)[2^(n-1)+1], n = 1..8);
%o (PARI) a(n) = {if(n<=2, n==1, (2*binomial(2^n-1, 2^(n-1)) + (2^n-1)*binomial(2^(n-1), 2^(n-2)))/2^n)} \\ _Andrew Howroyd_, Jan 09 2021
%Y Cf. A340312, A340263.
%K nonn
%O 1,3
%A _Peter Luschny_, Jan 06 2021