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A145170
G.f. A(x) satisfies A(x/A(x)) = 1/(1-x)^6.
4
1, 6, 57, 866, 18444, 492924, 15424611, 542166480, 20861518935, 864061112296, 38081996557383, 1771322835258594, 86425203984341130, 4402953230795279532, 233372023965531945057, 12832558973488295874402, 730347857708249147767893
OFFSET
0,2
LINKS
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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 03 2008
STATUS
approved