A368933 - OEIS

%I #10 Jan 10 2024 07:59:01

%S 1,2,7,30,143,729,3891,21471,121505,701316,4112751,24435424,146773582,

%T 889813460,5437598036,33459382065,207138653334,1289231982454,

%U 8062548100445,50637167131635,319255808742145,2019867936975125,12819928874057325,81603361510347675

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

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

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

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)*(1-x-x^5))/x)

%Y Cf. A236339, A368931, A368932.

%Y Cf. A276989, A366112.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 10 2024