A365764 - OEIS

%I #13 Sep 20 2023 10:00:33

%S 1,4,25,188,1563,13840,127972,1221260,11938471,118936100,1203155633,

%T 12325599632,127611357300,1333153669632,14035828918560,

%U 148773617605036,1586305110768863,17002975960876300,183102052226442475,1980078493171083292,21493846031259095539

%N Expansion of (1/x) * Series_Reversion( x*(1-x)^3/(1+x) ).

%H Seiichi Manyama, <a href="/A365764/b365764.txt">Table of n, a(n) for n = 0..940</a>

%F a(n) = (1/(n+1)) * Sum_{k=0..n} binomial(n+1,k) * binomial(4*n-k+2,n-k) = (1/(n+1)) * Sum_{k=0..n} binomial(3*n+k+2,k) * binomial(n+1,n-k).

%o (PARI) a(n) = sum(k=0, n, binomial(n+1, k)*binomial(4*n-k+2, n-k))/(n+1);

%Y Cf. A003169, A006318, A365765, A365766.

%Y Cf. A365751.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Sep 18 2023