A366097 Expansion of (1/x) * Series_Reversion( x*(1+x-x^3)/(1+x)^4 ).
1, 3, 12, 56, 287, 1564, 8896, 52217, 313955, 1923775, 11970066, 75427608, 480365740, 3086989128, 19992893796, 130363352003, 855099212950, 5638480905533, 37354602517624, 248515024509486, 1659620048332369, 11121368629141886, 74759777174598964
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n\3, binomial(n+k, k)*binomial(3*n-k+3, n-3*k))/(n+1);
Formula
a(n) = (1/(n+1)) * Sum_{k=0..floor(n/3)} binomial(n+k,k) * binomial(3*n-k+3,n-3*k).