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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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A242817 A295238 A256016 * A180255 A034218 A034237

Adjacent sequences:  A145167 A145168 A145169 * A145171 A145172 A145173

KEYWORD

nonn,changed

AUTHOR

Paul D. Hanna, Oct 03 2008

STATUS

approved

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Last modified November 14 22:32 EST 2019. Contains 329134 sequences. (Running on oeis4.)