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A145081 Row 1 of square table A145080; also equals row 1 of square table A145085. 6


%S 1,1,3,17,151,1901,31851,680265,17947631,571101141,21507723971,

%T 944074937297,47692346899367,2743393411694077,178059607814690011,

%U 12937663707325398297,1045119822694496457119,93294566475499260126949

%N Row 1 of square table A145080; also equals row 1 of square table A145085.

%C 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.

%C 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.

%H Paul D. Hanna, <a href="/A145081/b145081.txt">Table of n, a(n) for n = 0..60</a>

%H Emma Colaric, Ryan DeMuse, Jeremy L. Martin, and Mei Yin, <a href="https://arxiv.org/abs/2006.09321">Interval parking functions</a>, arXiv:2006.09321 [math.CO], 2020.

%F 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.

%F 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.

%o (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)

%o (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)

%o (PARI) a(n)=local(A=1); for(k=0, n-1, A=exp(intformal((n-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, A145082, A145083, A145084, A145085, A145086.

%K nonn

%O 0,3

%A _Paul D. Hanna_, Sep 30 2008

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