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%I #25 Jun 24 2021 11:35:16
%S 1,3,14,65,294,1302,5676,24453,104390,442442,1864356,7818538,32657884,
%T 135950700,564306840,2336457645,9652643910,39800950530,163830074100,
%U 673327275390,2763494696820,11327881630260,46381659765480,189711966348450,775232392541724
%N a(n)=f(n,n-2) where f is given in A034261.
%C Divisible by the Catalan numbers, by the explicit formula. - _F. Chapoton_, Jun 24 2021
%F a(n) = binomial(2*n-2,n-1)/n * (n^2-n+1).
%F a(n) = binomial(2*n-2,n-1) + (n-1)*binomial(2*n-2,n).
%o (Sage)
%o [binomial(2*n-2,n-1)//n * (n**2-n+1) for n in range(1,8)]
%o (PARI) a(n) = binomial(2*n-2,n-1)/n * (n^2-n+1); \\ _Michel Marcus_, Jun 24 2021
%Y Cf. A000108, A002061, A034261, A344191, A344228.
%K nonn,easy
%O 1,2
%A _Clark Kimberling_
%E Corrected and extended by _N. J. A. Sloane_, Apr 21 2000
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