A145081 - OEIS

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

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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