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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

Table of n, a(n) for n=1..17.

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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Last modified May 22 14:27 EDT 2013. Contains 225551 sequences.