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Expansion of (1/x) * Series_Reversion( x * ((1-x)^4 + x) ).
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%I #9 Mar 23 2024 11:08:24

%S 1,3,12,49,179,441,-860,-23634,-229246,-1705649,-10757370,-57800600,

%T -246084657,-551185526,3612960360,66196180728,641858169138,

%U 4911870929096,31792139997384,172691510260794,711428107177975,1066704835555530,-18659356513414560

%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} (-1)^k * binomial(n+k,k) * binomial(5*n+3*k+3,n-k).

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

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

%Y Cf. A369124, A369216.

%K sign

%O 0,2

%A _Seiichi Manyama_, Mar 23 2024