OFFSET
0,6
EXAMPLE
Triangle starts:
[1]
[0, 1]
[0, 1, 10]
[0, 1, 84, 280]
[0, 1, 682, 9240, 15400]
[0, 1, 5460, 260260, 1401400, 1401400]
[0, 1, 43690, 7128576, 99379280, 285885600, 190590400]
MAPLE
CL := (f, x) -> PolynomialTools:-CoefficientList(f, x):
A291451_row := proc(n) exp(x*(exp(z)/3+2*exp(-z/2)*cos(z*sqrt(3)/2)/3-1)):
series(%, z, 66): CL((3*n)!*coeff(series(%, z, 3*(n+1)), z, 3*n), x) end:
for n from 0 to 7 do A291451_row(n) od;
# Alternative:
A291451row := proc(n) local P; P := proc(m, n) option remember;
if n = 0 then 1 else add(binomial(m*n, m*k)*P(m, n-k)*x, k=1..n) fi end:
CL(P(3, n), x); seq(%[k+1]/k!, k=0..n) end: # Peter Luschny, Sep 03 2018
MATHEMATICA
P[m_, n_] := P[m, n] = If[n == 0, 1, Sum[Binomial[m*n, m*k]*P[m, n - k]*x, {k, 1, n}]];
row[n_] := Module[{cl = CoefficientList[P[3, n], x]}, Table[cl[[k + 1]]/k!, {k, 0, n}]];
Table[row[n], {n, 0, 7}] // Flatten (* Jean-François Alcover, Jul 23 2019, after Peter Luschny *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Sep 07 2017
STATUS
approved