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%I #17 Aug 21 2023 08:22:57
%S 1,4,18,104,671,4624,33342,248412,1897219,14774152,116864936,
%T 936390692,7584216152,61992689940,510728310716,4236545121924,
%U 35354229533389,296604036437692,2500154435955614,21164005790766980,179841032283906149,1533499916749203208
%N G.f. satisfies A(x) = 1/(1 - x/(1 - x*A(x))^2)^4.
%H Seiichi Manyama, <a href="/A349021/b349021.txt">Table of n, a(n) for n = 0..1000</a>
%F If g.f. satisfies: A(x) = 1/(1 - x/(1 - x*A(x))^s)^t, then a(n) = Sum_{k=0..n} binomial(t*n-(t-1)*(k-1),k) * binomial(n+(s-1)*k-1,n-k)/(n-k+1).
%p A349021 := proc(n)
%p local s,t ;
%p s := 2 ;
%p t := 4;
%p add( binomial(t*n-(t-1)*(k-1),k) * binomial(n+(s-1)*k-1,n-k) /(n-k+1) ,k=0..n) ;
%p end proc:
%p seq(A349021(n),n=0..40) ; # _R. J. Mathar_, May 12 2022
%o (PARI) a(n, s=2, t=4) = sum(k=0, n, binomial(t*n-(t-1)*(k-1), k)*binomial(n+(s-1)*k-1, n-k)/(n-k+1));
%Y Cf. A006013, A109081, A161799.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Nov 06 2021
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