A371870 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n-k-1,n-2*k).

1, 1, 4, 14, 51, 189, 709, 2683, 10220, 39130, 150438, 580328, 2245004, 8705686, 33828704, 131688362, 513445147, 2004688605, 7836832057, 30670416703, 120153739079, 471143251989, 1848978071615, 7261781367389, 28540427527441, 112243216215879, 441693646453729

Offset

0,3

Links

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

Formula

a(n) = [x^n] 1/((1-x-x^2) * (1-x)^(n-1)).

a(n) ~ 4^n / sqrt(Pi*n). - Vaclav Kotesovec, Apr 16 2024

a(n) = A354267(2*n, n). - Peter Luschny, Apr 25 2024

Prog

(PARI) a(n) = sum(k=0, n\2, binomial(2*n-k-1, n-2*k));

Crossrefs

Cf. A072547, A114121, A354267.

Sequence in context: A211303 A247415 A292463 * A149488 A058692 A165813

Adjacent sequences: A371867 A371868 A371869 * A371871 A371872 A371873

Keyword

nonn,changed

Author

Seiichi Manyama, Apr 10 2024

Status

approved