A158834 A diagonal in the array A158825 of coefficients of successive iterations of x*C(x), where C(x) is the Catalan function (A000108).

1, 4, 30, 315, 4200, 67620, 1273668, 27454218, 666200106, 17968302638, 533188477536, 17261808531552, 605452449574320, 22870569475477112, 925663441858807096, 39964465820186753753, 1833332492818402014474

Offset

1,2

Comments

Triangle A158835 transforms A158833 into this sequence, where A158833 is the previous 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),...;
1,12,156,2106,29120,409682,5841836,84218134,1225314662,(17968302638),...; ...
where terms in parenthesis form the initial terms of this sequence.

Mathematica

a[n_] := Module[{x, F, G}, F = InverseSeries[x - x^2 + O[x]^(n+2)]; G = x; For[i = 1, i <= n+2, i++, G = (F /. x -> G)]; Coefficient[G, x, n]];
Array[a, 17] (* Jean-François Alcover, Jul 13 2018, from PARI *)

Prog

(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)}

Crossrefs

Cf. A158825, A158831, A158832, A158833.

Sequence in context: A239841 A145348 A052574 * A139086 A243244 A293022

Adjacent sequences: A158831 A158832 A158833 * A158835 A158836 A158837

Keyword

nonn

Author

Paul D. Hanna, Mar 28 2009

Status

approved