A158828 The 5th iteration of x*C(x) where C(x) is the Catalan function (A000108).

1, 5, 30, 195, 1330, 9380, 67844, 500619, 3755156, 28558484, 219767968, 1708590960, 13403300208, 105983648060, 844009565176, 6764300053390, 54525119251104, 441811163402124, 3597005618194848, 29412560840221272

Offset

1,2

Links

Table of n, a(n) for n=1..20.

Elżbieta Liszewska and Wojciech Młotkowski, Some relatives of the Catalan sequence, arXiv:1907.10725 [math.CO], 2019.

Formula

G.f.: Series_Reversion( F_5(x) ), where F_n(x) is the n-th iteration of x*(1 - x).

Series reversion of x -5*x^2 +20*x^3 -70*x^4 +220*x^5 -630*x^6 +1656*x^7 -4014*x^8 +8994*x^9 -18654*x^10 +35832*x^11 -63750*x^12 +105024*x^13 -160120*x^14 +225696*x^15 -293685*x^16 +352074*x^17 -387820*x^18 +391232*x^19 -359992*x^20 +300664*x^21 -226580*x^22 +152952*x^23 -91656*x^24 +48204*x^25 -21924*x^26 +8456*x^27 -2692*x^28 +680*x^29 -128*x^30 +16*x^31 -x^32. - R. J. Mathar, Aug 30 2021

a(n) = Sum_{0 = x_0 <= x_1 <= ... <= x_4 <= x_5 = n-1} Product_{k=0..4} (x_k + 1) * binomial(2*x_{k+1} - x_k + 1,x_{k+1} - x_k)/(2*x_{k+1} - x_k + 1). - Seiichi Manyama, May 25 2026

Prog

(PARI) {a(n)=local(F=serreverse(x-x^2+O(x^(n+1))), G=x); for(i=1, 5, G=subst(F, x, G)); polcoeff(G, n)}

Crossrefs

Row n=5 of A158825.

Cf. A158826, A158827, A158829.

Sequence in context: A038744 A098663 A265085 * A264910 A196471 A265279

Adjacent sequences: A158825 A158826 A158827 * A158829 A158830 A158831

Keyword

nonn

Author

Paul D. Hanna, Mar 28 2009

Status

approved