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

1, 1, 3, 17, 151, 1901, 31851, 680265, 17947631, 571101141, 21507723971, 944074937297, 47692346899367, 2743393411694077, 178059607814690011, 12937663707325398297, 1045119822694496457119, 93294566475499260126949

Offset

0,3

Comments

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.

Links

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

Emma Colaric, Ryan DeMuse, Jeremy L. Martin, and Mei Yin, Interval parking functions, arXiv:2006.09321 [math.CO], 2020.

Formula

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.

Prog

(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)
(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)
for(n=0, 20, print1(a(n), ", ")) \\ Paul D. Hanna, Jan 08 2014

Crossrefs

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

Sequence in context: A307375 A007767 A075820 * A020562 A193161 A364630

Adjacent sequences: A145078 A145079 A145080 * A145082 A145083 A145084

Keyword

nonn

Author

Paul D. Hanna, Sep 30 2008

Status

approved