A145170 G.f. A(x) satisfies A(x/A(x)) = 1/(1-x)^6.

1, 6, 57, 866, 18444, 492924, 15424611, 542166480, 20861518935, 864061112296, 38081996557383, 1771322835258594, 86425203984341130, 4402953230795279532, 233372023965531945057, 12832558973488295874402, 730347857708249147767893

Offset: 0

Author

Paul D. Hanna, Oct 03 2008

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 0..317

Crossrefs

Cf. A145167, A145168, A145169.

Programs

Maple

A[0]:= x -> 1+c*x:
for n from 1 to 20 do
  cc:= coeff(series(A[n-1](x/A[n-1](x))-1/(1-x)^6, x, n+1),x,n);
  A[n]:= unapply(eval(A[n-1](x),c=solve(cc,c))+c*x^(n+1),x);
od:
seq(coeff(A[20](x),x,j),j=0..20); # Robert Israel, Aug 19 2018

Mathematica

nmax = 16; sol = {a[0] -> 1};
Do[A[x_] = Sum[a[k] x^k, {k, 0, n}] /. sol; eq = CoefficientList[A[x/A[x]] - 1/(1 - x)^6 + O[x]^(n + 1), x] == 0 /. sol; sol = sol ~Join~ Solve[eq] [[1]], {n, 1, nmax}]; sol /. Rule -> Set;
a /@ Range[0, nmax] (* Jean-François Alcover, Nov 01 2019 *)

PARI

{a(n)=local(A=1+x+x*O(x^n),B);for(n=0,n,B=serreverse(x/A);A=1/(1-B)^6);polcoeff(A,n)}

Formula

Self-convolution 6th power of A145167.

Self-convolution cube of A145168.

Self-convolution square of A145169.