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A276666 a(n) = (n-1)*Catalan(n). 2

%I

%S -1,0,2,10,42,168,660,2574,10010,38896,151164,587860,2288132,8914800,

%T 34767720,135727830,530365050,2074316640,8119857900,31810737420,

%U 124718287980,489325340400,1921133836440,7547311500300,29667795388452,116686713634848,459183826803800

%N a(n) = (n-1)*Catalan(n).

%F a(n) = [x^n] (1-3*x)/(x*sqrt(1-4*x))-1/x.

%F a(n) = 4^n*(n-1)*hypergeom([3/2, -n], [2], 1).

%F a(n) = 4^n*(n-1)*JacobiP(n,1,-1/2-n,-1)/(n+1).

%F a(n) = (2*n)! [x^(2^n)]( BesselI(2,2*x) - (1+1/x)*BesselI(1,2*x) ).

%F a(n) = binomial(2*n,n) - 2*Catalan(n). (See _Geoffrey Critzer_'s formula in A024483).

%F a(n) = A056040(2*n) - 2*A057977(2*n).

%F a(n) = A056040(2*n)*(1-2/(n+1)) = (n^2-1)*(2*n)!/(n+1)!^2.

%F a(n) = A232500(2*n).

%F a(n) = a(n-1)*2*(n-1)*(2*n-1)/((n-2)*(n+1)) for n > 2. - _Chai Wah Wu_, Sep 12 2016

%F a(n) = A024483(n+1) for n>0. - _R. J. Mathar_, Sep 13 2016

%p f := (1-3*x)/(x*sqrt(1-4*x))-1/x:

%p series(f,x,29): seq(coeff(%,x,n), n=0..26);

%p A276666 := n -> (n^2-1)*(2*n)!/(n+1)!^2:

%p seq(A276666(n), n=0..26);

%t Table[(n - 1) CatalanNumber[n], {n, 0, 30}] (* _Vincenzo Librandi_, Sep 13 2016 *)

%o (Sage)

%o A276666 = lambda n: (n-1) * catalan_number(n)

%o print [A276666(n) for n in range(27)]

%o (MAGMA) [(n-1)*Catalan(n): n in [0..30]]; // _Vincenzo Librandi_, Sep 13 2016

%Y A024483 is a variant of this sequence.

%Y Cf. A000108, A000984, A051631, A056040, A057977, A232500.

%K sign

%O 0,3

%A _Peter Luschny_, Sep 12 2016

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Last modified June 19 19:11 EDT 2019. Contains 324222 sequences. (Running on oeis4.)