A301392 a(n) = Product_{k=1..L} hypergeom([-n, -n], [1], k) with L = 3.

1, 24, 1716, 171360, 19908420, 2520945504, 337515951696, 46988523863424, 6733620845342820, 986687339945804640, 147160710112066546896, 22266479585813841915264, 3409510715450350579710096, 527349554424095532928444800, 82268694346361937381278049600

Offset

0,2

Links

Table of n, a(n) for n=0..14.

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

Recurrence: (n-2)*(n-1)*n^3*(2*n - 5)*a(n) = 24*(n-2)*(n-1)*(2*n - 5)*(2*n - 1)^3*a(n-1) - 32*(n-2)*(2*n - 3)^2*(2*n - 1)*(25*n^2 - 75*n + 31)*a(n-2) + 384*(2*n - 5)^3*(2*n - 3)*(2*n - 1)^2*a(n-3) - 256*(n-3)*(2*n - 7)*(2*n - 5)*(2*n - 3)*(2*n - 1)^2*a(n-4). - Vaclav Kotesovec, Mar 26 2018

Maple

a := n -> mul(hypergeom([-n, -n], [1], k), k=1..3):
seq(simplify(a(k)), k=0..11);

Mathematica

a[n_] := Product[Hypergeometric2F1[-n, -n, 1, k], {k, 1, 3}];
Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Mar 20 2018 *)

Crossrefs

With the parameter L in the name: A000012 (L=0), A000984 (L=1), A268555 (L=2), this seq. (L=3), A301393 (L=4).

Sequence in context: A187634 A229430 A054777 * A084224 A348589 A227257

Adjacent sequences: A301389 A301390 A301391 * A301393 A301394 A301395

Keyword

nonn

Author

Peter Luschny, Mar 20 2018

Status

approved