OFFSET
0,5
LINKS
Emma Colaric, Ryan DeMuse, Jeremy L. Martin, and Mei Yin, Interval parking functions, arXiv:2006.09321 [math.CO], 2020.
FORMULA
Row e.g.f.s satisfy: R(n,x) = exp( n*Integral R(n+1,x) dx ).
Row e.g.f.s satisfy: R(n,x) = 1 + n*Integral R(n,x)*R(n+1,x) dx.
Row e.g.f.s satisfy: R'(n,x)/R(n,x) = n*R(n+1,x) with R(n,0) = 1.
EXAMPLE
Table begins:
1,1,3,17,151,1901,31851,680265,17947631,571101141,21507723971,...;
1,2,10,86,1090,18710,412402,11253638,370191682,14385490550,...;
1,3,21,243,4029,88491,2450085,82648611,3313381293,154912893243,...;
1,4,36,524,10756,288764,9667476,390576684,18591797156,1023871865244,...;
1,5,55,965,23635,750905,29542255,1393871405,77048083675,...;
1,6,78,1602,45606,1674546,75766566,4093500690,258080963526,...;
1,7,105,2471,80185,3341975,171024777,10417654023,738359218457,...;
1,8,136,3608,131464,6132536,350289640,23758306136,1870826922568,...;
1,9,171,5049,204111,10537029,664636851,49684658769,4304660616711,...;
1,10,210,6830,303370,17172110,1185578010,96858862110,9158464815050,...;
1,11,253,8987,435061,26794691,2009911981,178179417515,18260617937221,..;
1,12,300,11556,605580,40316340,3265094652,312177663108,34472306461932,.;
PROG
(PARI) {T(n, k)=local(A=vector(n+k+2, j, 1+j*x)); for(i=0, n+k+1, for(j=0, n+k, m=n+k+1-j; A[m]=exp(m*intformal(A[m+1]+x*O(x^k))))); k!*polcoeff(A[n], k, x)}
for(n=1, 10, for(k=0, 10, print1(T(n, k), ", ")); print(""))
(PARI) {T(n, k)=local(A=vector(n+k+2, j, 1+j*x)); for(i=0, n+k+1, for(j=0, n+k, m=n+k+1-j; A[m]=exp(intformal(A[m+1]^m+x*O(x^k))))); k!*polcoeff(A[n+1]^n, k, x)}
for(n=1, 10, for(k=0, 10, print1(T(n, k), ", ")); print(""))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Sep 30 2008
STATUS
approved