A368974 - OEIS

A368974

Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^3)^2 ).

%I #14 Jan 13 2024 10:45:45

%S 1,3,15,89,580,4009,28857,213967,1622869,12531090,98171544,778364379,

%T 6233789872,50355710215,409790010350,3356429972859,27647745771339,

%U 228890532343859,1903475080613014,15893483726218904,133190665385526309,1119863488613216952

%N Expansion of (1/x) * Series_Reversion( x * (1-x) * (1-x+x^3)^2 ).

%H Seiichi Manyama, <a href="/A368974/b368974.txt">Table of n, a(n) for n = 0..1000</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/3)} (-1)^k * binomial(2*n+k+1,k) * binomial(4*n-2*k+2,n-3*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x+x^3)^2)/x)

%o (PARI) a(n, s=3, t=2, u=1) = sum(k=0, n\s, (-1)^k*binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);

%Y Cf. A368970, A368976.

%Y Cf. A368966.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 10 2024