|
|
A046757
|
|
Triangle of coefficients of certain polynomials (exponents in decreasing order).
|
|
1
|
|
|
1, 2, 1, 5, 5, 1, 30, 30, 10, 1, 272, 272, 102, 17, 1, 3250, 3250, 1300, 260, 26, 1, 47952, 47952, 19980, 4440, 555, 37, 1, 840350, 840350, 360150, 85750, 12250, 1050, 50, 1, 17039360, 17039360, 7454720, 1863680, 291200, 29120, 1820, 65, 1, 392203458
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n, n)= 1, a(n, m)= (1+n^2)*binomial(n, m)*n^(n-m-2), n>m >= 0, else 0.
|
|
EXAMPLE
|
{1}; {2,1}; {5,5,1}; {30,30,10,1}; {272,272,102,17,1}; .... E.g. third row {5,5,1} corresponds to polynomial q{3,x)= 5*x^2+5*x+1.
|
|
CROSSREFS
|
x*p(k-1, -x)/q(k, -x), with the row polynomials p(n, x) from triangle A033842(n, m) is for k=1..5 G.f. for A000079 (powers of two), A039717, A043553, A045624, A046088, respectively.
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|