A268548 The diagonal of 1/((1-x-y-z -u)*(1-u-z-x z)).

1, 44, 5061, 771000, 134309890, 25316919264, 5026804760628, 1035584197646064, 219294892124599500, 47438623242735925200, 10438147961521506499845, 2328874968375190922731200, 525637255621548684267389736, 119802332975029272210072348800

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..200

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.

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

Formula

From Vaclav Kotesovec, Jul 01 2016: (Start)

Recurrence: 16*n^3*(2*n + 1)^2*(4*n - 1)*(4*n + 1)*(37345*n^5 - 170391*n^4 + 303508*n^3 - 263678*n^2 + 111816*n - 18536)*a(n) = (9816992185*n^12 - 49686077183*n^11 + 99053358610*n^10 - 93579615936*n^9 + 32313594569*n^8 + 13219591749*n^7 - 14764491100*n^6 + 3112939874*n^5 + 953756168*n^4 - 467159208*n^3 + 20288512*n^2 + 14747520*n - 1843200)*a(n-1) - 72*(2*n - 1)*(3*n - 4)^2*(3*n - 2)^2*(4*n - 5)*(4*n - 3)*(37345*n^5 + 16334*n^4 - 4606*n^3 - 2050*n^2 + 145*n + 64)*a(n-2).

a(n) ~ 2^(8*n + 7/2) / (7 * Pi^(3/2) * n^(3/2)).

(End)

Maple

A268548 := proc(n)
    1/(1-x-y-z-u)/(1-u-z-x*z) ;
    coeftayl(%, x=0, n) ;
    coeftayl(%, y=0, n) ;
    coeftayl(%, z=0, n) ;
    coeftayl(%, u=0, n) ;
end proc:
seq(A268548(n), n=0..40) ; # R. J. Mathar, Mar 10 2016

Mathematica

f = 1/((1 - x - y - z - u)*(1 - u - z - x z));
a[n_] := Fold[SeriesCoefficient[#1, {#2, 0, n}] &, f, {x, y, z, u}];
Array[a, 40, 0] (* Jean-François Alcover, Dec 03 2017 *)

Crossrefs

Sequence in context: A304460 A332562 A078279 * A203974 A266853 A323315

Adjacent sequences: A268545 A268546 A268547 * A268549 A268550 A268551

Keyword

nonn

Author

N. J. A. Sloane, Feb 29 2016

Status

approved