|
|
A168288
|
|
T(n,k) = 3*A046802(n+1,k+1) - 2*A007318(n,k), triangle read by rows (0 <= k <= n).
|
|
8
|
|
|
1, 1, 1, 1, 5, 1, 1, 15, 15, 1, 1, 37, 87, 37, 1, 1, 83, 373, 373, 83, 1, 1, 177, 1389, 2609, 1389, 177, 1, 1, 367, 4791, 15263, 15263, 4791, 367, 1, 1, 749, 15787, 80285, 134647, 80285, 15787, 749, 1, 1, 1515, 50529, 393657, 1033401, 1033401, 393657, 50529
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: 3*(1 - x)*exp(t)/(1 - x*exp(t*(1 - x))) - 2*exp(t*(1 + x)).
|
|
EXAMPLE
|
Triangle begins:
1;
1, 1;
1, 5, 1;
1, 15, 15, 1;
1, 37, 87, 37, 1;
1, 83, 373, 373, 83, 1;
1, 177, 1389, 2609, 1389, 177, 1;
1, 367, 4791, 15263, 15263, 4791, 367, 1;
1, 749, 15787, 80285, 134647, 80285, 15787, 749, 1;
|
|
MATHEMATICA
|
p[t_] = 3*(1 - x)*Exp[t]/(1 - x*Exp[t*(1 - x)]) - 2*Exp[t*(1 + x)];
Table[CoefficientList[FullSimplify[n!*SeriesCoefficient[Series[p[t], {t, 0, n}], n]], x], {n, 0, 10}]//Flatten
|
|
PROG
|
(Maxima) A046802(n, k) := sum(binomial(n - 1, r)*sum(j!*(-1)^(k - j - 1)*stirling2(r, j)*binomial(r - j, k - j - 1), j, 0, k - 1), r, k - 1, n - 1)$
T(n, k) := 3*A046802(n + 1, k + 1) - 2*binomial(n, k)$
create_list(T(n, k), n, 0, 10, k, 0, n);
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|