A378567 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n+3*k-1,n-k).
1, 1, 11, 88, 715, 5951, 50288, 429696, 3702987, 32125390, 280211701, 2454992618, 21588647392, 190444368401, 1684556756320, 14935618142768, 132695019071499, 1181070210132582, 10529299131757754, 94005323670592130, 840373149466892965, 7521508912742542806
Offset: 0
Keywords
Programs
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Mathematica
a[n_]:=SeriesCoefficient[ 1/(1 - x/(1 - x)^4)^n,{x,0,n}]; Array[a,22,0] (* Stefano Spezia, Dec 01 2024 *) -
PARI
a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(n+3*k-1, n-k));
Formula
a(n) = [x^n] 1/(1 - x/(1 - x)^4)^n.