A268546 From the diagonal of 1/((1 - x - y - u - z)*(1 - u - z - u z)).

1, 42, 4878, 748020, 130916310, 24762428460, 4929691760532, 1017691904736936, 215868481746244470, 46762158493003813860, 10301263206399347906724, 2300606339065015587232536, 519698719167846252879954564, 118536490001488475468485495800

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, 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)

D-finite with recurrence: (n-1)^2*n^3*(3*n - 1)*(3*n + 1)*(771750*n^7 - 8478225*n^6 + 39164195*n^5 - 98482265*n^4 + 145417589*n^3 - 125974978*n^2 + 59265082*n - 11685188)*a(n) = 2*(n-1)^2*(2*n - 1)*(1819786500*n^11 - 21123811800*n^10 + 104661527985*n^9 - 288341545275*n^8 + 481409553112*n^7 - 495872377658*n^6 + 303633537261*n^5 - 96245217427*n^4 + 7691237430*n^3 + 2702246656*n^2 - 317062544*n - 16813440)*a(n-1) - 4*(2*n - 3)*(2*n - 1)*(88023489750*n^12 - 1187056160325*n^11 + 7007020117965*n^10 - 23737551707835*n^9 + 50789159978443*n^8 - 71020649752291*n^7 + 64633979350247*n^6 - 36533794634477*n^5 + 11213428304727*n^4 - 1067031625504*n^3 - 195871773612*n^2 + 4820925232*n + 5452816320)*a(n-2) + 32*(2*n - 5)*(2*n - 3)*(2*n - 1)*(3*n - 7)*(3*n - 5)*(4*n - 9)*(4*n - 7)*(771750*n^7 - 3075975*n^6 + 4501595*n^5 - 2823415*n^4 + 577229*n^3 + 59524*n^2 - 7292*n - 2040)*a(n-3).

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

(End)

Maple

A268546 := proc(n)
    1/(1-x-y-u-z)/(1-u-z-u*z) ;
    coeftayl(%, x=0, n) ;
    coeftayl(%, y=0, n) ;
    coeftayl(%, z=0, n) ;
    coeftayl(%, u=0, n) ;
end proc:
seq(A268546(n), n=0..40) ; # R. J. Mathar, Mar 10 2016

Mathematica

f = 1/((1 - x - y - u - z)*(1 - u - z - u z));
a[n_] := Fold[SeriesCoefficient[#1, {#2, 0, n}]&, f, {x, y, z, u}];
Array[a, 14, 0] (* Jean-François Alcover, Dec 03 2017 *)

Crossrefs

Sequence in context: A294974 A263057 A048538 * A102967 A091545 A101630

Adjacent sequences: A268543 A268544 A268545 * A268547 A268548 A268549

Keyword

nonn

Author

N. J. A. Sloane, Feb 29 2016

Status

approved