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%I #26 Nov 17 2022 07:59:57
%S 1,1,4,9,56,190,1704,7644,93120,516240,8136000,53523360,1047548160,
%T 7961241600,187132377600,1611967392000,44311886438400,426483893606400,
%U 13428757601280000,142790947407360000,5066854992138240000,58981696577556480000,2328441680297779200000
%N a(n) = n! * Sum_{k=0..floor(n/2)} 1/binomial(n-k, k).
%H Seiichi Manyama, <a href="/A358446/b358446.txt">Table of n, a(n) for n = 0..449</a>
%F E.g.f.: (2*x+1)/((x-1)*(x+1)*(x^2-x-1))-(x*log((1-x)^2*(x+1)))/(-x^2+x+1)^2.
%F a(n) ~ n! * (3 + (-1)^n)/2. - _Vaclav Kotesovec_, Nov 17 2022
%F a(n) = Sum_{k=0..floor(n/2)} A143216(n, k)/A344391(n, k). - _Peter Luschny_, Nov 17 2022
%p egf := (2*x+1)/((x-1)*(x+1)*(x^2-x-1))-(x*log((1-x)^2*(x+1)))/(-x^2+x+1)^2:
%p ser := series(egf, x, 22): seq(n!*coeff(ser, x, n), n = 0..20); # _Peter Luschny_, Nov 17 2022
%o (Maxima)
%o a(n):=factorial(n)*sum(1/binomial(n-k,k),k,0,floor(n/2));
%o (SageMath)
%o def A358446(n):
%o return sum(A143216(n, k) // A344391(n, k) for k in range((n+2)//2))
%o print([A358446(n) for n in range(23)]) # _Peter Luschny_, Nov 17 2022
%Y Cf. A003149, A143216, A344391.
%K nonn
%O 0,3
%A _Vladimir Kruchinin_, Nov 16 2022
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