A378554 a(n) = Sum_{k=0..n} 4^(n-k) * binomial(n+k-1,k) * binomial(k/2,n-k).
1, 1, 7, 28, 171, 846, 4942, 26580, 153363, 856900, 4939682, 28140476, 162676878, 936947116, 5436375532, 31526252208, 183571246659, 1069552636950, 6247183319938, 36524006501180, 213899020967786, 1253905101529080, 7359775341696180, 43237184121401400
Offset: 0
Keywords
Programs
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Mathematica
a[n_]:=SeriesCoefficient[1/(1 - x*(1 + 4*x)^(1/2))^n,{x,0,n}]; Array[a,24,0] (* Stefano Spezia, Nov 30 2024 *) -
PARI
a(n) = sum(k=0, n, 4^(n-k)*binomial(n+k-1, k)*binomial(k/2, n-k));
Formula
a(n) = [x^n] 1/(1 - x*(1 + 4*x)^(1/2))^n.