|
|
A361355
|
|
Triangle read by rows: T(n,k) is the number of simple series-parallel matroids on [n] with rank k, 1 <= k <= n.
|
|
2
|
|
|
1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 15, 1, 0, 0, 0, 0, 75, 1, 0, 0, 0, 0, 735, 280, 1, 0, 0, 0, 0, 0, 9345, 938, 1, 0, 0, 0, 0, 0, 76545, 77805, 2989, 1, 0, 0, 0, 0, 0, 0, 1865745, 536725, 9285, 1, 0, 0, 0, 0, 0, 0, 13835745, 27754650, 3334870, 28446, 1, 0
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,13
|
|
LINKS
|
|
|
FORMULA
|
E.g.f.: A(x,y) = log(1 + B(x,y)) where B(x,y) is the e.g.f. of A361353.
E.g.f.: A(x,y) = log(B(log(1 + x), y)/(1 + x)) where B(x,y) is the e.g.f. of A359985.
|
|
EXAMPLE
|
Triangle begins:
1;
0, 0;
0, 1, 0;
0, 0, 1, 0;
0, 0, 15, 1, 0;
0, 0, 0, 75, 1, 0;
0, 0, 0, 735, 280, 1, 0;
0, 0, 0, 0, 9345, 938, 1, 0;
0, 0, 0, 0, 76545, 77805, 2989, 1, 0;
...
|
|
PROG
|
(PARI) \\ B gives A359985 as e.g.f.
B(n)= {exp(x*(1+y) + y*intformal(serreverse(log(1 + x*y + O(x^n))/y + log(1 + x + O(x^n)) - x)))}
T(n) = {my(v=Vec(serlaplace(log(subst(B(n), x, log(1 + x + O(x*x^n)))/(1 + x))))); vector(#v, n, Vecrev(v[n]/y, n))}
{ my(A=T(9)); for(i=1, #A, print(A[i])) }
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|