0,3

Let R(n,x) be the e.g.f. of row n of square table A145080, then the

e.g.f.s satisfy: R(n,x) = exp( n*Integral R(n+1,x) dx ) for n>=1.

Let S(n,x) = R(n,x)^(1/n) 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.

Paul D. Hanna, Table of n, a(n) for n=0..60

E.g.f.: A(x) = R(1,x) = exp( Integral R(2,x) dx ) where R(n,x) is the e.g.f. of row n of square table A145080.

E.g.f.: A(x) = G'(x)/G(x) where G(x) is the e.g.f. of A145086, which is row 0 of square table A145085.

(PARI) {a(n)=local(A=vector(n+2, j, 1+j*x)); for(i=0, n+1, for(j=0, n, m=n+1-j; A[m]=exp(m*intformal(A[m+1]+x*O(x^n))))); n!*polcoeff(A[1], n, x)}

(PARI) {a(n)=local(A=vector(n+2, j, 1+j*x)); for(i=0, n+1, for(j=0, n, m=n+1-j; A[m]=exp(intformal(A[m+1]^(m+1)+x*O(x^n))))); n!*polcoeff(A[1], n, x)}

Cf. A145080, A145082, A145083, A145084; A145085, A145086.

Sequence in context: A135750 A007767 A075820 this_sequence A020562 A135751 A168441

Adjacent sequences: A145078 A145079 A145080 this_sequence A145082 A145083 A145084

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Sep 30 2008