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A145084 Row 4 of square table A145080. 6

%I #2 Mar 30 2012 18:37:15

%S 1,4,36,524,10756,288764,9667476,390576684,18591797156,1023871865244,

%T 64308208060916,4553899456432844,360155907603064196,

%U 31561618500966519484,3044291843751868832596,321353247687162678690924

%N Row 4 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(4,x) = exp( 4*Integral R(5,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)^4 where G(x) is the e.g.f. of A145089, which is row 4 of square table A145085.

%o (PARI) {a(n)=local(A=vector(n+5,j,1+j*x)); for(i=0,n+4,for(j=0,n,m=n+4-j;A[m]=exp(m*intformal(A[m+1]+x*O(x^n))))); n!*polcoeff(A[4],n,x)}

%o (PARI) {a(n)=local(A=vector(n+5,j,1+j*x)); for(i=0,n+4,for(j=0,n,m=n+4-j;A[m]=exp(intformal(A[m+1]^(m+1)+x*O(x^n))))); n!*polcoeff(A[4]^4,n,x)}

%Y Cf. A145080, A145081, A145082, A145083; A145085, A145089.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Oct 01 2008

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