A158827 The 4th iteration of x*C(x) where C(x) is the Catalan function (A000108).

1, 4, 20, 110, 640, 3870, 24084, 153306, 993978, 6544242, 43652340, 294469974, 2006018748, 13784115468, 95444016984, 665407010349, 4667570034444, 32922870719664, 233389493503968, 1662048903052380, 11885333877149532

Offset: 1

Author

Paul D. Hanna, Mar 28 2009

Keywords

• nonn

Links

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

Crossrefs

Cf. A158825, A158826, A158828, A158829.

Programs

PARI

{a(n)=local(F=serreverse(x-x^2+O(x^(n+1))),G=x); for(i=1,4,G=subst(F,x,G));polcoeff(G,n)}

Formula

Series reversion of 1 -4*x +12*x^2 -30*x^3 +64*x^4 -118*x^5 +188*x^6 -258*x^7 +302*x^8 -298*x^9 +244*x^10 -162*x^11 +84*x^12 -32*x^13 +8*x^14 -x^15. - R. J. Mathar, Aug 30 2021