A378566 a(n) = Sum_{k=0..n} binomial(n+k-1,k) * binomial(n+2*k-1,n-k).
1, 1, 9, 64, 465, 3456, 26082, 199060, 1532313, 11875015, 92528414, 724187982, 5689127886, 44834549501, 354289977750, 2806262293824, 22273793685609, 177113634045858, 1410633764438967, 11251419724586850, 89860413370562730, 718528004169570925
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n, binomial(n+k-1, k)*binomial(n+2*k-1, n-k));
Formula
a(n) = [x^n] 1/(1 - x/(1 - x)^3)^n.