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%I #15 Nov 12 2022 02:10:25
%S 1,3,14,94,728,6220,56960,549412,5517746,57235402,609632284,
%T 6638455152,73653980850,830429715762,9494320306104,109882451968812,
%U 1285515149382226,15184272319785322,180901975355930990,2171974459996885630,26260944994924397048,319547523490735463404
%N a(n) = Sum_{j=0..n} (-1)^j*binomial(2*n - j, j)*c(n - j + 1)^2, where c(n) is the n-th Catalan number.
%F G.f.: ((1-14*x+x^2)^(1/2)*(x+1)^2*hypergeom([-1/2, 3/2],[1],-16*x/(1-14*x+x^2))-x^3-7*x^2-7*x-1)/(4*x^2). - _Mark van Hoeij_, Nov 11 2022
%p c := n -> binomial(2*n, n)/(n + 1):
%p A358118 := n -> add((-1)^j*binomial(2*n-j, j)*c(n-j+1)^2, j = 0..n):
%p seq(A358118(n), n = 0..21);
%o (Python)
%o from math import comb
%o def A358118(n): return sum((-1 if j&1 else 1)*comb((n<<1)-j,j)*(comb(n-j+1<<1,n-j+1)//(n-j+2))**2 for j in range(n+1)) # _Chai Wah Wu_, Nov 11 2022
%Y Cf. A000108, A358119.
%K nonn
%O 0,2
%A _Peter Luschny_, Nov 11 2022
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