OFFSET
0,6
LINKS
Paul D. Hanna, Table of n, a(n) for n = 0..1080
FORMULA
Row e.g.f.s satisfy: R(n,x) = exp( Integral R(n+1,x)^(n+1) dx ).
Row e.g.f.s satisfy: R(n,x) = 1 + Integral R(n,x)*R(n+1,x)^(n+1) dx.
Row e.g.f.s satisfy: R'(n,x)/R(n,x) = R(n+1,x)^(n+1) with R(n,0) = 1.
EXAMPLE
Table begins:
1,1,2,7,39,322,3723,57577,1147188,28557909,866222535,31362744620,...;
1,1,3,17,151,1901,31851,680265,17947631,571101141,21507723971,...;
1,1,4,31,373,6250,136711,3740137,124143598,4887140221,224203589593,...;
1,1,5,49,741,15457,416661,13908049,557865765,26296627233,...;
1,1,6,71,1291,32186,1030491,40606281,1911466016,105145651821,...;
1,1,7,97,2059,59677,2211823,100479577,5431432483,341787359269,...;
1,1,8,127,3081,101746,4283511,220384585,13453788426,953539677861,...;
1,1,9,161,4393,162785,7672041,440897697,30000376553,2365207145121,...;
1,1,10,199,6031,247762,12921931,820341289,61561430380,5344379824933,...;
1,1,11,241,8031,362221,20710131,1439328361,118089834231,11194348009941,...;
1,1,12,287,10429,512282,31860423,2405825577,214232473478,22019097106029,..;
1,1,13,337,13261,704641,47357821,3860734705,370824076621,41076472798081,..;
1,1,14,391,16563,946570,68362971,5983992457,616668950808,73237232298621,..;
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(intformal(A[m+1]^m+x*O(x^k))))); k!*polcoeff(A[n+1], k, x)}
for(n=0, 10, for(k=0, 10, print1(T(n, k), ", ")); print(""))
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Paul D. Hanna, Oct 01 2008
EXTENSIONS
Entry corrected by Paul D. Hanna, Sep 22 2020
STATUS
approved