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A276666 a(n) = (n-1)*Catalan(n). 2
-1, 0, 2, 10, 42, 168, 660, 2574, 10010, 38896, 151164, 587860, 2288132, 8914800, 34767720, 135727830, 530365050, 2074316640, 8119857900, 31810737420, 124718287980, 489325340400, 1921133836440, 7547311500300, 29667795388452, 116686713634848, 459183826803800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..26.

FORMULA

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

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

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

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

a(n) = binomial(2*n,n) - 2*Catalan(n). (See Geoffrey Critzer's formula in A024483).

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

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

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

a(n) = a(n-1)*2*(n-1)*(2*n-1)/((n-2)*(n+1)) for n > 2. - Chai Wah Wu, Sep 12 2016

a(n) = A024483(n+1) for n>0. - R. J. Mathar, Sep 13 2016

MAPLE

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

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

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

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

MATHEMATICA

Table[(n - 1) CatalanNumber[n], {n, 0, 30}] (* Vincenzo Librandi, Sep 13 2016 *)

PROG

(Sage)

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

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

(MAGMA) [(n-1)*Catalan(n): n in [0..30]]; // Vincenzo Librandi, Sep 13 2016

CROSSREFS

A024483 is a variant of this sequence.

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

Sequence in context: A192695 A181052 A024483 * A302524 A084180 A020988

Adjacent sequences:  A276663 A276664 A276665 * A276667 A276668 A276669

KEYWORD

sign

AUTHOR

Peter Luschny, Sep 12 2016

STATUS

approved

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Last modified May 26 19:44 EDT 2019. Contains 323597 sequences. (Running on oeis4.)