A378464 a(n) = Sum_{k=0..floor(n/3)} binomial(n+k-1,k) * binomial(2*n-1,n-3*k).
1, 1, 3, 13, 63, 306, 1473, 7085, 34239, 166459, 813618, 3994200, 19678233, 97239130, 481740885, 2392004853, 11900655999, 59312062026, 296071376307, 1479998924447, 7407613846698, 37118966710076, 186195636158436, 934889598483048, 4698229684691913, 23629859054461331
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(n+k-1, k)*binomial(2*n-1, n-3*k));
Formula
a(n) = [x^n] 1/(1 - x - x^3/(1 - x)^2)^n.