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

0,2

Links

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

Formula

Self-convolution 6th power of A145167.

Self-convolution cube of A145168.

Self-convolution square of A145169.

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 *)

Prog

(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)}

Crossrefs

Cf. A145167, A145168, A145169.

Sequence in context: A295238 A256016 A361291 * A180255 A371033 A034218

Adjacent sequences: A145167 A145168 A145169 * A145171 A145172 A145173

Keyword

nonn

Author

Paul D. Hanna, Oct 03 2008

Status

approved