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A255673 Coefficients of A(x), which satisfies: A(x) = 1 + x*A(x)^3 + x^2*A(x)^6. 2
1, 1, 4, 21, 127, 833, 5763, 41401, 305877, 2309385, 17739561, 138197876, 1089276972, 8670856834, 69606939717, 562879492551, 4580890678781, 37490975387565, 308369889858450, 2547741413147700, 21133987935358776, 175947462569886786, 1469656053534121804 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

This sequence is the next after A001006 and A006605.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = 1/(3*n+1) * Sum_{k=0..n} (-1)^k * binomial(3*n+1, k) * binomial(6*n+2-2*k, n-k). (conjectured)

G.f. A(x) satisfies A(x) = G(x*A(x)), where G is g.f. of A006605.

G.f. A(x) satisfies A(x) = H(x*A(x)^2), where H is g.f. of A001006.

EXAMPLE

A(x) = 1 + x + 4*x^2 + 21*x^3 + 127*x^4 + 833*x^5 + 5763*x^6 ...

MAPLE

a:= n-> coeff(series(RootOf(1-A+x*A^3+x^2*A^6, A), x, n+1), x, n):

seq(a(n), n=0..30);  # Alois P. Heinz, Jul 15 2015

# second Maple program:

a:= proc(n) option remember; `if`(n<2, 1, 9*(((3*n-1))*

     (2*n-1)*(3*n-2)*(9063*n^4-18126*n^3+8403*n^2+660*n-280)*a(n-1)

     +(27*(n-1))*(3*n-1)*(3*n-4)*(3*n-2)*(3*n-5)*(57*n^2-2)*a(n-2))

      /((5*(5*n+2))*(5*n-1)*(5*n+1)*(5*n-2)*n*(57*n^2-114*n+55)))

    end:

seq(a(n), n=0..30);  # Alois P. Heinz, Jul 16 2015

CROSSREFS

Cf. A001006, A006605.

Sequence in context: A032326 A281581 A007345 * A099250 A293192 A232956

Adjacent sequences:  A255670 A255671 A255672 * A255674 A255675 A255676

KEYWORD

nonn

AUTHOR

Werner Schulte, Jul 10 2015

EXTENSIONS

More terms from Alois P. Heinz, Jul 15 2015

STATUS

approved

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Last modified February 21 19:26 EST 2018. Contains 299422 sequences. (Running on oeis4.)