A369102 - OEIS

%I #10 Jan 13 2024 10:45:04

%S 1,4,26,204,1772,16408,158752,1585968,16235472,169423232,1795611168,

%T 19275231872,209140483328,2289981517312,25271472702464,

%U 280795784911616,3138701648319744,35270318924758016,398215386792574464,4515067063939210240,51388662166213954560

%N Expansion of (1/x) * Series_Reversion( x * ((1-x)^4-x^4) ).

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

%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/4)} binomial(n+k,k) * binomial(5*n+3,n-4*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*((1-x)^4-x^4))/x)

%o (PARI) a(n) = sum(k=0, n\4, binomial(n+k, k)*binomial(5*n+3, n-4*k))/(n+1);

%Y Cf. A097188, A151374.

%Y Cf. A063021.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 13 2024