A276989 Reversion of x - x^2 - x^6.

1, 1, 2, 5, 14, 43, 140, 474, 1650, 5863, 21170, 77441, 286372, 1068790, 4020704, 15230470, 58044354, 222401745, 856235030, 3310615055, 12849946406, 50051007940, 195571906140, 766413504375, 3011469930300, 11862075827007, 46830440626612, 185271557066226

Offset: 1

Author

Benedict W. J. Irwin, Sep 24 2016

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..1615
• Vladimir Kruchinin, The method for obtaining expressions for coefficients of reverse generating functions, arXiv:1211.3244 [math.CO], 2012.

Programs

Maple

S:= series(RootOf(x-x^2-x^6-t,x),t,41):
seq(coeff(S,t,i),i=1..40); # Robert Israel, Nov 04 2024

Mathematica

Table[Sum[Binomial[n-1-4*j,j]Binomial[2*n-4*j-2,n-1],{j,0,(n-1)/2}]/n, {n, 1, 25}]

Formula

a(n) = (Sum_{j=0..(n-1)/2} C(n-1-4*j,j)*C(2*n-4*j-2,n-1))/n.