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A365766 Expansion of (1/x) * Series_Reversion( x*(1-x)^5/(1+x) ).

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%I A365766 #13 Sep 20 2023 10:00:26
%S A365766 1,6,56,626,7721,101322,1387648,19606874,283711805,4183074796,
%T A365766 62618441024,949174260118,14539621490403,224721722650224,
%U A365766 3500129695446816,54882906729334378,865664769346769005,13725517938819785298,218639429113140366968
%N A365766 Expansion of (1/x) * Series_Reversion( x*(1-x)^5/(1+x) ).
%H A365766 Seiichi Manyama, <a href="/A365766/b365766.txt">Table of n, a(n) for n = 0..811</a>
%F A365766 a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(6*n-k+4,n-k) = (1/(n+1)) * Sum_{k=0..n} binomial(5*n+k+4,k) * binomial(n+1,n-k).
%o A365766 (PARI) a(n) = sum(k=0, n, binomial(n+1, k)*binomial(6*n-k+4, n-k))/(n+1);
%Y A365766 Cf. A003169, A006318, A365764, A365765.
%Y A365766 Cf. A365753.
%K A365766 nonn
%O A365766 0,2
%A A365766 _Seiichi Manyama_, Sep 18 2023