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A359761
a(n) = binomial(4*n, 2*n)*(2*n)!/(2^n*n!).
1
1, 6, 210, 13860, 1351350, 174594420, 28109701620, 5421156741000, 1218404977539750, 312723944235202500, 90252130306279441500, 28929910132721937339000, 10197793321784482911997500, 3920659309406065045704885000, 1632674555274097086889962825000, 732091270584905133761459330730000
OFFSET
0,2
FORMULA
a(n) = (2^(3*n)*Gamma(2*n + 1/2))/(sqrt(Pi)*Gamma(n + 1)).
a(n) = A359760(4*n, 2*n), the central terms of the triangle without the zeros.
a(n) = A001448(n)*A001147(n). - R. J. Mathar, Jan 25 2023
D-finite with recurrence n*a(n) -2*(4*n-1)*(4*n-3)*a(n-1)=0. - R. J. Mathar, Jan 25 2023
MAPLE
a := binomial(4*n, 2*n)*(2*n)!/(2^n*n!):
seq(a(n), n = 0..15);
CROSSREFS
Cf. A359760.
Sequence in context: A183287 A087639 A028350 * A238685 A346017 A099788
KEYWORD
nonn,easy
AUTHOR
Peter Luschny, Jan 14 2023
STATUS
approved