A073768 Triangle of coefficients of Bateman polynomial n!Z_n(-x).

1, 1, 2, 2, 12, 6, 6, 72, 90, 20, 24, 480, 1080, 560, 70, 120, 3600, 12600, 11200, 3150, 252, 720, 30240, 151200, 201600, 94500, 16632, 924, 5040, 282240, 1905120, 3528000, 2425500, 698544, 84084, 3432, 40320, 2903040, 25401600, 62092800, 58212000, 24216192, 4708704, 411840, 12870

Offset

0,3

Links

Table of n, a(n) for n=0..44.

Example

{1};
{1, 2};
{2, 12, 6};
{6, 72, 90, 20};
{24, 480, 1080, 560, 70}; ...
2!Z_2(-x) = 2+12x+6x^2.

Maple

A073768_row := proc(n) n!*hypergeom([-n, n+1], [1, 1], -x);
PolynomialTools:-CoefficientList(simplify(%), x) end:
seq(A073768_row(n), n=0..8): ListTools[FlattenOnce]([%]); # Peter Luschny, Jan 31 2016

Mathematica

T[n_, k_] := n! (n+k)! / (n-k)! / k!^3;
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 04 2019 *)

Prog

(PARI) {T(n, k) = if( k<0 || k>n, 0, n! * (n+k)! / (n-k)! / k!^3)}

Crossrefs

A073767 gives row sums.

Sequence in context: A279179 A279470 A013605 * A278534 A256120 A024538

Adjacent sequences: A073765 A073766 A073767 * A073769 A073770 A073771

Keyword

nonn,tabl

Author

Michael Somos, Aug 08 2002

Status

approved