G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^3 * x^k / A(x)^k] * x^n/n ).

Terms

a(0) =1a(1) =1a(2) =2a(3) =5a(4) =10a(5) =22a(6) =58a(7) =150a(8) =392a(9) =1097a(10) =3139a(11) =9069a(12) =26903a(13) =81299a(14) =248305a(15) =768521a(16) =2407340a(17) =7607947a(18) =24248690a(19) =77906841a(20) =251995121a(21) =820096599a(22) =2684160567a(23) =8830103123a(24) =29183369411a(25) =96865043941a(26) =322780531149