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A145083 Row 3 of square table A145080. 6


%S 1,3,21,243,4029,88491,2450085,82648611,3313381293,154912893243,

%T 8322387603093,507658268093811,34817646211022301,2662987196578490187,

%U 225556061819586894597,21030571231219899162435

%N Row 3 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(3,x) = exp( 3*Integral R(4,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)^3 where G(x) is the e.g.f. of A145088, which is row 3 of square table A145085.

%o (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],n,x)

%o (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]^3,n,x)

%o (PARI) a(n)=local(A=1); for(k=0, n-1, A=exp(intformal((n-k+2)*(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, A145082, A145084, A145085, A145088.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 01 2008

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Last modified January 20 01:18 EST 2022. Contains 350467 sequences. (Running on oeis4.)