A365766 - OEIS

%I #13 Sep 20 2023 10:00:26

%S 1,6,56,626,7721,101322,1387648,19606874,283711805,4183074796,

%T 62618441024,949174260118,14539621490403,224721722650224,

%U 3500129695446816,54882906729334378,865664769346769005,13725517938819785298,218639429113140366968

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

%H Seiichi Manyama, <a href="/A365766/b365766.txt">Table of n, a(n) for n = 0..811</a>

%F 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 (PARI) a(n) = sum(k=0, n, binomial(n+1, k)*binomial(6*n-k+4, n-k))/(n+1);

%Y Cf. A003169, A006318, A365764, A365765.

%Y Cf. A365753.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 18 2023