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A034275
a(n)=f(n,n-2) where f is given in A034261.
2
1, 3, 14, 65, 294, 1302, 5676, 24453, 104390, 442442, 1864356, 7818538, 32657884, 135950700, 564306840, 2336457645, 9652643910, 39800950530, 163830074100, 673327275390, 2763494696820, 11327881630260, 46381659765480, 189711966348450, 775232392541724
OFFSET
1,2
COMMENTS
Divisible by the Catalan numbers, by the explicit formula. - F. Chapoton, Jun 24 2021
FORMULA
a(n) = binomial(2*n-2,n-1)/n * (n^2-n+1).
a(n) = binomial(2*n-2,n-1) + (n-1)*binomial(2*n-2,n).
PROG
(Sage)
[binomial(2*n-2, n-1)//n * (n**2-n+1) for n in range(1, 8)]
(PARI) a(n) = binomial(2*n-2, n-1)/n * (n^2-n+1); \\ Michel Marcus, Jun 24 2021
CROSSREFS
KEYWORD
nonn,easy
EXTENSIONS
Corrected and extended by N. J. A. Sloane, Apr 21 2000
STATUS
approved