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%I #8 Sep 27 2023 10:07:03
%S 1,3,16,104,750,5769,46373,384885,3273118,28372354,249762585,
%T 2226782078,20065651123,182457467898,1672073116401,15427427247088,
%U 143191280370438,1336062703751262,12524930325385008,117910257665608080,1114233543986585741
%N Expansion of (1/x) * Series_Reversion( x*(1-x)^4/(1-x+x^2) ).
%F a(n) = (1/(n+1)) * Sum_{k=0..floor(n/2)} binomial(n+1,k) * binomial(4*n-k+2,n-2*k).
%o (PARI) a(n) = sum(k=0, n\2, binomial(n+1, k)*binomial(4*n-k+2, n-2*k))/(n+1);
%Y Cf. A005043, A109081, A366049.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Sep 27 2023
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