%I #13 Jan 13 2024 10:45:53
%S 1,4,24,170,1320,10868,93199,823548,7446480,68567202,640757920,
%T 6061477500,57933260067,558580920160,5426644737984,53069206438226,
%U 522004849765080,5161083186971000,51262685633583970,511272660117154692,5118240198221249088
%N Expansion of (1/x) * Series_Reversion( x * (1-x)^2 * (1-x+x^2)^2 ).
%H Seiichi Manyama, <a href="/A368975/b368975.txt">Table of n, a(n) for n = 0..973</a>
%H <a href="/index/Res#revert">Index entries for reversions of series</a>
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} (-1)^k * binomial(2*n+k+1,k) * binomial(5*n-k+3,n-2*k).
%o (PARI) my(N=30, x='x+O('x^N)); Vec(serreverse(x*(1-x)^2*(1-x+x^2)^2)/x)
%o (PARI) a(n, s=2, t=2, u=2) = sum(k=0, n\s, (-1)^k*binomial(t*(n+1)+k-1, k)*binomial((t+u+1)*(n+1)-(s-1)*k-2, n-s*k))/(n+1);
%Y Cf. A368969, A368973.
%Y Cf. A368967.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Jan 10 2024
|