A158831 - OEIS

A158831

A diagonal in the array A158825 of coefficients of successive iterations of x*C(x), where C(x) is the Catalan function (A000108).

1, 1, 6, 54, 640, 9380, 163576, 3305484, 75915708, 1952409954, 55573310936, 1734182983962, 58863621238500, 2159006675844616, 85088103159523296, 3585740237981536700, 160894462797493581048, 7658326127259130753070

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OFFSET

1,3

COMMENTS

Triangle A158835 transforms this sequence into A158832, the next diagonal in A158825.

LINKS

Table of n, a(n) for n=1..18.

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

Cf. A158825, A158832, A158833, A158834.

Sequence in context: A367471 A367475 A081132 * A034001 A084062 A292633

Adjacent sequences: A158828 A158829 A158830 * A158832 A158833 A158834

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Mar 28 2009

STATUS

approved