1,2

Triangle A158835 transforms A158833 into this sequence, where A158833 is the previous 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),...;

1,12,156,2106,29120,409682,5841836,84218134,1225314662,(17968302638),...; ...

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+2, G=subst(F, x, G)); polcoeff(G, n)}

Cf. A158825, A158831, A158832, A158833.

Sequence in context: A088794 A145348 A052574 this_sequence A139086 A128329 A006149

Adjacent sequences: A158831 A158832 A158833 this_sequence A158835 A158836 A158837

nonn

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