A379084 a(n) = Sum_{k=0..floor(n/2)} binomial(2*n+k-1,k) * binomial(2*n+k,n-2*k).
1, 2, 10, 62, 394, 2562, 16966, 113794, 770458, 5254658, 36046470, 248449104, 1719175846, 11935608518, 83100064834, 579994824042, 4056746450106, 28428354905268, 199550820571858, 1402832286126650, 9875127071717694, 69599814539512900, 491081313666879968, 3468458841769675496
Offset: 0
Keywords
Programs
-
PARI
a(n) = sum(k=0, n\2, binomial(2*n+k-1, k)*binomial(2*n+k, n-2*k));
Formula
a(n) = [x^n] 1/( 1/(1 + x) - x^2 )^(2*n).
a(n) == 0 (mod 2) for n>0.