A371574 G.f. satisfies A(x) = ( 1 + x*A(x)^(5/2) * (1 + x*A(x)) )^2.
1, 2, 13, 106, 986, 9902, 104641, 1146654, 12910674, 148462310, 1736178005, 20584835962, 246874102771, 2989580399330, 36504669373240, 448960388422126, 5556453433915920, 69150493021938224, 864833621158491876, 10863849369160145222, 137011477676531989664
Offset: 0
Keywords
Programs
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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));
Formula
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).
G.f.: A(x) = B(x)^2 where B(x) is the g.f. of A365186.