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