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%I A358791 #18 Apr 15 2023 06:26:57
%S A358791 1,1,4,8,52,156,1536,6144,84096,420480,7453440,44720640,974972160,
%T A358791 6824805120,176504832000,1412038656000,42224136192000,380017225728000,
%U A358791 12893605517721600,128936055177216000,4892595136708608000
%N A358791 a(n) = n!*Sum_{m=0..floor(n/2)} binomial(n,2*m)^(-1).
%H A358791 Seiichi Manyama, <a href="/load/view.php?a=aHR0cDovL29laXMub3JnL0EzNTg3OTEvYjM1ODc5MS50eHQ">Table of n, a(n) for n = 0..449</a>
%F A358791 E.g.f.: (1/2)*( log(1+x)/x^2-log(1-x)*(x^2+4*x-4)/(x^4-4*x^3+4*x^2)+6/(x^3-2*x^2-x+2) ).
%F A358791 P-recursive: 2*n*(n + 2)*(n - 2)*(3*n - 2)*a(n) = n*(n + 1)*(n + 2)*(n - 2)*(3*n - 2)*a(n-1) + 2*n^3*(n - 1)*(n - 2)*(3*n + 4)*a(n-2) - n^3*(n - 1)^2*(n - 2)*(3*n + 4)*a(n-3) with a(0) = a(1) = 1 and a(2) = 4. - _Peter Bala_, Apr 13 2023
%o A358791 (Maxima)
%o A358791 a(n):=n!*sum(1/binomial(n,2*m),m,0,floor(n/2));
%o A358791 (PARI) a(n) = n!*sum(m=0, n\2, 1/binomial(n, 2*m)); \\ _Michel Marcus_, Dec 01 2022
%Y A358791 Cf. A003149.
%K A358791 nonn
%O A358791 0,3
%A A358791 _Vladimir Kruchinin_, Dec 01 2022

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