A368967 - OEIS

A368967

Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x-x^2)^2 ).

%I #17 Jan 14 2024 08:56:37

%S 1,4,28,238,2244,22568,237199,2574276,28627224,324503718,3735672880,

%T 43555658640,513277420803,6103767231712,73153216133600,

%U 882708243017414,10714917867247020,130752597362068496,1603069096165788706,19737123968746454284,243930175282166574432

%N Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x-x^2)^2 ).

%H Seiichi Manyama, <a href="/A368967/b368967.txt">Table of n, a(n) for n = 0..893</a>

%H <a href="/index/Res#revert">Index entries for reversions of series</a>

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(2*n+k+1,k) * binomial(5*n-k+3,n-2*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x-x^2)^2)/x)

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

%Y Cf. A368961, A368965.

%Y Cf. A368968.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 10 2024