cp's OEIS Frontend

A386615 a(n) = Sum_{k=0..n-1} binomial(6*k,k) * binomial(6*n-6*k,n-k-1).

%I A386615 #19 Jul 29 2025 08:39:31
%S A386615 0,1,18,291,4550,70065,1069872,16251694,246010014,3714826350,
%T A386615 55993450830,842823848448,12672667549488,190381643518855,
%U A386615 2858101359683400,42882348756992220,643085584745669134,9640075656634321770,144457232389535563980,2164044325920832653825,32409930873969839549610
%N A386615 a(n) = Sum_{k=0..n-1} binomial(6*k,k) * binomial(6*n-6*k,n-k-1).
%F A386615 G.f.: g^2 * (g-1)/(6-5*g)^2 where g=1+x*g^6.
%F A386615 G.f.: g/((1-g) * (1-6*g)^2) where g*(1-g)^5 = x.
%F A386615 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.
%F A386615 a(n) = Sum_{k=0..n-1} 5^(n-k-1) * binomial(6*n+1,k).
%F A386615 a(n) = Sum_{k=0..n-1} 6^(n-k-1) * binomial(5*n+k+1,k).
%o A386615 (PARI) a(n) = sum(k=0, n-1, binomial(6*k, k)*binomial(6*n-6*k, n-k-1));
%Y A386615 Cf. A079679, A386368, A386567, A386616.
%Y A386615 Cf. A008549, A386611, A386613.
%K A386615 nonn
%O A386615 0,3
%A A386615 _Seiichi Manyama_, Jul 27 2025