OFFSET
1,3
EXAMPLE
Table of coefficients in the i-th iteration of x*Catalan(x):
(1);
1,(1),2,5,14,42,132,429,1430,4862,16796,58786,208012,...;
1,2,(6),21,80,322,1348,5814,25674,115566,528528,2449746,...;
1,3,12,(54),260,1310,6824,36478,199094,1105478,6227712,...;
1,4,20,110,(640),3870,24084,153306,993978,6544242,43652340,...;
1,5,30,195,1330,(9380),67844,500619,3755156,28558484,...;
1,6,42,315,2464,19852,(163576),1372196,11682348,100707972,...;
1,7,56,476,4200,38052,351792,(3305484),31478628,303208212,...;
1,8,72,684,6720,67620,693048,7209036,(75915708),807845676,...;
1,9,90,945,10230,113190,1273668,14528217,167607066,(1952409954),...; ...
where terms in parenthesis form the initial terms of this sequence.
MATHEMATICA
nmax = 18;
g[x_] := Module[{y}, Expand[Normal[(1 - Sqrt[1 - 4*y])/2 + O[y]^(nmax+2)] /. y -> x][[1 ;; nmax+1]]];
T = Table[Nest[g, x, n] // CoefficientList[#, x]& // Rest, {n, 1, nmax+1}];
Prepend[Diagonal[T, 1], 1] (* Jean-François Alcover, Jul 13 2018 *)
PROG
(PARI) {a(n)=local(F=serreverse(x-x^2+O(x^(n+2))), G=x); for(i=1, n-1, G=subst(F, x, G)); polcoeff(G, n)}
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Mar 28 2009
STATUS
approved