A145082 - OEIS

%I #6 Jul 19 2016 11:21:16

%S 1,2,10,86,1090,18710,412402,11253638,370191682,14385490550,

%T 649929193426,33702126998438,1984615178100514,131531988461545238,

%U 9736285622878908466,799603624057192515014,72433928850731333868034

%N Row 2 of square table A145080.

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

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

%F E.g.f.: A(x) = R(2,x) = exp( 2*Integral R(3,x) dx ) where R(n,x) is the e.g.f. of row n of square table A145080.

%F E.g.f.: A(x) = G(x)^2 where G(x) is the e.g.f. of A145087, which is row 2 of square table A145085.

%o (PARI) a(n)=local(A=vector(n+3,j,1+j*x)); for(i=0,n+2,for(j=0,n,m=n+2-j;A[m]=exp(m*intformal(A[m+1]+x*O(x^n))))); n!*polcoeff(A[2],n,x)

%o (PARI) a(n)=local(A=vector(n+3,j,1+j*x)); for(i=0,n+2,for(j=0,n,m=n+2-j;A[m]=exp(intformal(A[m+1]^(m+1)+x*O(x^n))))); n!*polcoeff(A[2]^2,n,x)

%o (PARI) a(n)=local(A=1); for(k=0, n-1, A=exp(intformal((n+1-k)*(A+x*O(x^n))))); n!*polcoeff(A, n)

%o for(n=0, 20, print1(a(n), ", ")) \\ _Paul D. Hanna_, Jan 08 2014

%Y Cf. A145080, A145081, A145083, A145084, A145085, A145087.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 01 2008