_Paul D. Hanna (pauldhanna(AT)juno.com), _, Oct 01 2008

E.g.f.: A(x) = R(3,x)^(1/3) = exp( Integral R(4,x) dx ) where R(3,x) = e.g.f. of A145083, and R(4,x) = e.g.f. of A145084.

nonn,new

nonn

Row 3 of square table A145085.

1, 1, 5, 49, 741, 15457, 416661, 13908049, 557865765, 26296627233, 1431946482453, 88859040485585, 6214831383604709, 485449303578082273, 42025472165413172501, 4005872618389765500113, 418072369437989483917349

0,3

Let S(n,x) be the e.g.f. of row n of square table A145085, then the e.g.f.s satisfy: S(n,x) = exp( Integral S(n+1,x)^(n+1) dx ) for n>=0.

E.g.f.: A(x) = S(3,x) = exp( Integral S(4,x)^4 dx ) where S(n,x) is the e.g.f. of row n of square table A145085.

E.g.f.: A(x) = R(3,x)^(1/3) = exp( Integral R(4,x) dx ) where R(3,x) = e.g.f. of A145083, and R(4,x) = e.g.f. of A145084.

(PARI) {a(n)=local(A=vector(n+4, j, 1+j*x)); for(i=0, n+3, for(j=0, n, m=n+3-j; A[m]=exp(m*intformal(A[m+1]+x*O(x^n))))); n!*polcoeff(A[3]^(1/3), n, x)}

(PARI) {a(n)=local(A=vector(n+4, j, 1+j*x)); for(i=0, n+3, for(j=0, n, m=n+3-j; A[m]=exp(intformal(A[m+1]^(m+1)+x*O(x^n))))); n!*polcoeff(A[3], n, x)}

Cf. A145085, A145086, A145087, A145089; A145080, A145083.

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Oct 01 2008

approved