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%I #13 Mar 29 2024 15:21:48
%S 1,2,13,106,986,9902,104641,1146654,12910674,148462310,1736178005,
%T 20584835962,246874102771,2989580399330,36504669373240,
%U 448960388422126,5556453433915920,69150493021938224,864833621158491876,10863849369160145222,137011477676531989664
%N G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) * (1 + x*A(x)) )^2.
%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(s*k,n-k)/(t*k+u*(n-k)+r).
%F G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A365186.
%o (PARI) a(n, r=2, s=1, t=5, u=2) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(s*k, n-k)/(t*k+u*(n-k)+r));
%Y Cf. A000108, A143927, A365153, A368961, A371575.
%Y Cf. A365186.
%K nonn
%O 0,2
%A _Seiichi Manyama_, Mar 28 2024