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Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 - x^4) ).
1

%I #11 Mar 23 2024 10:56:41

%S 1,3,12,55,272,1413,7599,41933,236053,1350093,7822620,45817390,

%T 270815730,1613300978,9676131942,58380176644,354081959367,

%U 2157570900137,13201923181308,81084900544971,499711105642851,3089163236655363,19150916212748940,119031956868317285

%N Expansion of (1/x) * Series_Reversion( x / ((1+x)^3 - 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)} (-1)^k * binomial(n+1,k) * binomial(3*n-3*k+3,n-4*k).

%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x/((1+x)^3-x^4))/x)

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

%Y Cf. A107264, A127897, A371428.

%Y Cf. A369159.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Mar 23 2024