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A276013 Diagonal of (1 - 9 x y) / ((1 - 3 y - 2 x + 3 y^2 + 8 x^2 y) * (1 - u - z) * (1 - v - w)). 1
1, 12, 864, 100800, 14112000, 2139830784, 338341183488, 54913641209856, 9080061146956800, 1523231914913280000, 258557709598427086848, 44324863067728222027776, 7663322563977594870300672, 1334677098876385703362560000, 233951210561895726160281600000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

"The corresponding (order-five) linear differential operator is not homomorphic to its adjoint, even with an algebraic extension, and its differential Galois group is SL(5,C)." (see A. Bostan link).

LINKS

Gheorghe Coserea, Table of n, a(n) for n = 0..33

A. Bostan, S. Boukraa, J.-M. Maillard, J.-A. Weil, Diagonals of rational functions and selected differential Galois groups, arXiv preprint arXiv:1507.03227 [math-ph], 2015, Eq. (36).

Jacques-Arthur Weil, Supplementary Material for the Paper "Diagonals of rational functions and selected differential Galois groups"

FORMULA

a(n) = [(xyzuvw)^n] (1-9*x*y)/((1 - 3*y - 2*x + 3*y^2 + 8*x^2*y) * (1-u-z) * (1-v-w)).

From Vaclav Kotesovec, Dec 03 2017: (Start)

Recurrence: (n-1)^2*n^3*(3*n - 5)*a(n) = 24*(n-1)^2*(2*n - 1)^2*(3*n - 4)*(3*n - 2)*a(n-1) - 384*(2*n - 3)^2*(2*n - 1)^2*(3*n - 5)*(3*n - 2)*a(n-2).

a(n) ~ Gamma(1/3) * 2^(6*n - 7/3) * 3^(n + 1/2) / (Pi^2 * n^(4/3)). (End)

EXAMPLE

1 + 12*x + 864*x^2 + 100800*x^3 + ...

MAPLE

diag_coeff := proc(expr, n)

    local var := [seq(indets(expr))], nvar := numelems(var);

    coeftayl(expr, var=[seq(0, i=1..nvar)], [seq(n, i=1..nvar)])

end proc:

pxy := (1 - 3*y - 2*x + 3*y^2 + 9*x^2*y):

expr := (1 - 9*x*y)/(pxy * (1-u-z-u*z) * (1-v-w)):

[seq(diag_coeff(expr, i), i=0..14)];

MATHEMATICA

f = (1 - 9 x y)/((1 - 3y - 2x + 3 y^2 + 8 x^2 y)*(1 - u - z)*(1 - v - w));

a[n_] := Fold[SeriesCoefficient[#1, {#2, 0, n}] &, f, {x, y, z, u, v, w}];

Array[a, 40, 0] (* Jean-Fran├žois Alcover, Dec 03 2017 *)

CROSSREFS

Cf. A004987, A268549, A268545-A268555.

Sequence in context: A275568 A271433 A140412 * A116225 A214313 A306642

Adjacent sequences:  A276010 A276011 A276012 * A276014 A276015 A276016

KEYWORD

nonn

AUTHOR

Gheorghe Coserea, Aug 16 2016

STATUS

approved

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)