A369216 - OEIS

%I #10 Jan 16 2024 08:33:01

%S 1,5,44,479,5827,75887,1034980,14593794,211031650,3112385177,

%T 46636714566,707983562624,10865572966703,168306274609798,

%U 2627854427929448,41314461126179272,653481096161664690,10391753978329136808,166040704868503173384

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

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

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

%o (PARI) my(N=20, x='x+O('x^N)); Vec(serreverse(x*((1-x)^4-x))/x)

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

%Y Cf. A151374, A249924, A369215.

%Y Cf. A369102.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 16 2024