A371820 a(n) = Sum_{k=0..floor(n/3)} (-1)^k * binomial(2*n+2,n-3*k).
1, 4, 15, 55, 200, 726, 2640, 9636, 35343, 130339, 483395, 1802901, 6760781, 25482643, 96506229, 367077447, 1401772536, 5372120718, 20653929804, 79634421312, 307826528346, 1192608522258, 4629875048634, 18006340509702, 70142823370656, 273633773330844
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, (-1)^k*binomial(2*n+2, n-3*k));
Formula
a(n) = [x^n] 1/(((1-x)^3+x^3) * (1-x)^n).
a(n) = binomial(2*(1+n), n)*hypergeom([1, (1-n)/3, (2-n)/3, -n/3], [1+n/3, (4+n)/3, (5+n)/3], 1). - Stefano Spezia, Apr 07 2024
a(n) ~ 2^(2*n+1) / sqrt(Pi*n). - Vaclav Kotesovec, Apr 19 2024