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%I #9 Dec 09 2024 10:58:43
%S 1,4,10,32,119,468,1934,8256,36135,161276,731158,3357748,15587004,
%T 73021200,344786056,1639145180,7839483967,37692820908,182087119582,
%U 883358016328,4301799946048,21021519618724,103049029114618,506608410994868,2497162797380145,12338908560964968
%N G.f. A(x) satisfies A(x) = ( 1 + x/(1 - x*A(x)^(3/4)) )^4.
%F G.f.: A(x) = (1 + x*B(x))^4 where B(x) is the g.f. of A364742.
%F If g.f. satisfies A(x) = ( 1 + x*A(x)^(t/r) / (1 - x*A(x)^(u/r))^s )^r, then a(n) = r * Sum_{k=0..n} binomial(t*k+u*(n-k)+r,k) * binomial(n+(s-1)*k-1,n-k)/(t*k+u*(n-k)+r).
%o (PARI) a(n, r=4, s=1, t=0, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));
%Y Cf. A364742, A365119, A378730.
%Y Cf. A005554, A378801.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Dec 09 2024