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 A158833 A diagonal in the array A158825 of coefficients of successive iterations of x*C(x), where C(x) is the Catalan function (A000108). 6
 1, 3, 20, 195, 2464, 38052, 693048, 14528217, 344320262, 9100230282, 265305808404, 8456446272144, 292528760419440, 10913859037065560, 436812586581170976, 18668379209883807385, 848499254768957476312 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS EXAMPLE 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. 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 Cf. A158825, A158831, A158832, A158834. Sequence in context: A108206 A120485 A087152 * A054361 A052595 A052590 Adjacent sequences:  A158830 A158831 A158832 * A158834 A158835 A158836 KEYWORD nonn AUTHOR Paul D. Hanna, Mar 28 2009 STATUS approved

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