A386615 a(n) = Sum_{k=0..n-1} binomial(6*k,k) * binomial(6*n-6*k,n-k-1).
0, 1, 18, 291, 4550, 70065, 1069872, 16251694, 246010014, 3714826350, 55993450830, 842823848448, 12672667549488, 190381643518855, 2858101359683400, 42882348756992220, 643085584745669134, 9640075656634321770, 144457232389535563980, 2164044325920832653825, 32409930873969839549610
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=0, n-1, binomial(6*k, k)*binomial(6*n-6*k, n-k-1));
Formula
G.f.: g^2 * (g-1)/(6-5*g)^2 where g=1+x*g^6.
G.f.: g/((1-g) * (1-6*g)^2) where g*(1-g)^5 = x.
a(n) = Sum_{k=0..n-1} binomial(6*k+l,k) * binomial(6*n-6*k-l,n-k-1) for every real number l.
a(n) = Sum_{k=0..n-1} 5^(n-k-1) * binomial(6*n+1,k).
a(n) = Sum_{k=0..n-1} 6^(n-k-1) * binomial(5*n+k+1,k).