A378552 a(n) = Sum_{k=0..n} 9^k * binomial(n/3+k-1,k) * binomial(n-1,n-k).
1, 3, 51, 900, 16455, 307833, 5850000, 112445112, 2180050215, 42552000000, 835075676361, 16461248223588, 325696500000000, 6464447754891285, 128654307202482420, 2566472490000000000, 51302899404879842343, 1027391467409893403745, 20607804108000000000000
Offset: 0
Keywords
Programs
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Mathematica
a[n_]:=SeriesCoefficient[1/(1 - 9*x/(1-x))^(n/3),{x,0,n}]; Array[a,19,0] (* Stefano Spezia, Nov 30 2024 *) -
PARI
a(n) = sum(k=0, n, 9^k*binomial(n/3+k-1, k)*binomial(n-1, n-k));
Formula
a(n) = [x^n] 1/(1 - 9*x/(1-x))^(n/3).