OFFSET
0,6
EXAMPLE
Triangle starts:
[1]
[0, 1]
[0, 1, 35]
[0, 1, 495, 5775]
[0, 1, 8255, 450450, 2627625]
[0, 1, 130815, 35586525, 727476750, 2546168625]
[0, 1, 2098175, 2941884000, 181262956875, 1932541986375, 4509264634875]
MAPLE
CL := (f, x) -> PolynomialTools:-CoefficientList(f, x):
A291452_row := proc(n) exp(x*(cos(z)+cosh(z)-2)/2):
series(%, z, 88): CL((4*n)!*coeff(series(%, z, 4*(n+1)), z, 4*n), x) end:
for n from 0 to 7 do A291452_row(n) od;
# Alternative:
A291452row := 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(4, 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[4, n], x]}, Table[cl[[k + 1]]/k!, {k, 0, n}]];
Table[row[n], {n, 0, 6}] // Flatten (* Jean-François Alcover, Jul 23 2019, after Peter Luschny *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Sep 07 2017
STATUS
approved