1,2

Triangle A158835 transforms A158832 into this sequence, where A158832 is the previous diagonal in A158825.

Triangle A158835 transforms this sequence into A158834, the next diagonal in A158825.

Array of coefficients in the i-th iteration of x*Catalan(x):

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,...;

1,10,110,1265,14960,180510,2212188,27454218,(344320262),...;

1,11,132,1650,21164,276562,3666520,49181418,666200106,(9100230282),...; ...

where terms in parenthesis form the initial terms of this sequence.

(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)}

Cf. A158825, A158831, A158832, A158834.

Sequence in context: A108206 A120485 A087152 this_sequence A054361 A052595 A052590

Adjacent sequences: A158830 A158831 A158832 this_sequence A158834 A158835 A158836

nonn

Paul D. Hanna (pauldhanna(AT)juno.com), Mar 28 2009