A369297 - OEIS

%I #14 Feb 15 2024 04:12:48

%S 1,2,7,31,153,806,4440,25266,147364,876282,5292527,32378125,200218715,

%T 1249456536,7858638756,49766595855,317051378103,2030589300596,

%U 13066646029059,84439101344619,547746622599561,3565472378360110,23282050305073680,152466688160732190

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

%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)} binomial(n+k,k) * binomial(3*n-3*k+1,n-3*k).

%F a(n) = (1/(n+1)) * [x^n] 1/( (1-x)^2 * (1-x^3) )^(n+1). - _Seiichi Manyama_, Feb 14 2024

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

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

%Y Cf. A063030, A369265.

%Y Cf. A370273.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jan 18 2024