|
|
A291451
|
|
Triangle read by rows, expansion of e.g.f. exp(x*(exp(z)/3 + 2*exp(-z/2)* cos(z*sqrt(3)/2)/3 - 1)), nonzero coefficients of z.
|
|
11
|
|
|
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, 0, 1, 349524, 193360720, 6600492080, 42549306800, 76045569600, 36212176000
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,6
|
|
LINKS
|
|
|
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}]];
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|