A034275 - OEIS

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A034275

a(n)=f(n,n-2) where f is given in A034261.

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

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OFFSET

1,2

COMMENTS

Divisible by the Catalan numbers, by the explicit formula. - F. Chapoton, Jun 24 2021

LINKS

Table of n, a(n) for n=1..25.

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

Cf. A000108, A002061, A034261, A344191, A344228.

Sequence in context: A161131 A247978 A026592 * A240008 A151322 A373450

Adjacent sequences: A034272 A034273 A034274 * A034276 A034277 A034278

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling

EXTENSIONS

Corrected and extended by N. J. A. Sloane, Apr 21 2000

STATUS

approved