A382886 G.f. A(x) satisfies A(x) = 1/( 1 - x * (1+x)^2 * A(x) )^3.
1, 3, 21, 154, 1248, 10710, 95751, 882297, 8320812, 79927938, 779303829, 7692585186, 76726084742, 772066751871, 7828529324175, 79908510600542, 820435635949686, 8467306916189517, 87791572491261912, 914032693961190414, 9552050623400554164, 100162810727306404897
Offset: 0
Keywords
Programs
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PARI
a(n, r=3, s=2, t=4, u=0) = 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
G.f. A(x) satisfies A(x) = ( 1 + x * (1+x)^2 * A(x)^(4/3) )^3.
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.: B(x)^3, where B(x) is the g.f. of A378786.